Session CP8: Poster Session II: Reconnection and Non-Neutral I; Spheromaks and MCX; MFC Diagnostics; Simulation: Algorithm; Simulation: Kinetic/Edge

Boundary conditions in magnetic reconnection

Magnetic reconnection in the collisionless regime is studied on the Versatile Toroidal Facility (VTF) at MIT. The VTF device supports experiments with two distinct sets of boundary conditions: an ``open'' configuration for which the field lines intersect the vacuum vessel walls, and a ``closed'' configuration for which the magnetic field lines form closed loops inside the device. In the open configuration all electrons follow trapped trajectories. Our experimental and numerical studies reveal how these trapped electrons control the size of the reconnection region and mediate fast reconnection. This mechanism is found to be consistent observations by the WIND spacecraft in the deep magnetotail [1,2]. In the new closed configuration a parameter regime of special interest exists where the reconnection process appears in rapid bursts [3]. The vast differences in the experimental results for the two configurations emphasize the importance of boundary conditions. It suggests that there may not exist one unified theory for reconnection.\\[0ex] [1] M Oieroset, et al., (2002) Phys. Rev. Lett. 89, 195001.\\[0ex] [2] J Egedal, et al., (2005) Phys. Rev. Lett. 94, 025006.\\[0ex] [3] J Egedal, et al., (2007) Phys. Rev. Lett. 98, 015003.   

Experimental study of fast fluctuations and turbulence during magnetic reconnection events on the VTF experiment

We present measurements of electrostatic fluctuations during reconnection events on the VTF experiment at MIT. Because we have found a regime in VTF where the reconnection is ``bursty'' in time [1], it is an ideal experiment for answering the long-standing question of whether current-driven turbulence plays an important role in the reconnection process. Our measurement system consists of high-bandwidth, impedance-matched Langmuir probes, digitized by a fast oscilloscope. Broadband fluctuations are observed, extending up to $f_{ce}$ ($\simeq$~1.5~GHz, $f_{pe}/f_{ce} \simeq 10$), coincident with reconnection events both in time and space. Arrays of probes and standard cross-correlation analysis provide wavelength measurements. Non-linear phenomena, such as discrete positive potential spikes, traveling at $\sim$2-3~v$_{te}$ and with spatial width 1-2~mm ($\simeq 50-100~\lambda_{De}$) are also observed coincident with large reconnection events. Finally, we will discuss various instability mechanisms, with insight from a recently-installed electron energy analyzer.\\[1ex] [1] J. Egedal, \textit{et al}. (2007). PRL \textbf{98}, 015003.   

Three-Dimensional Magnetic and Electrostatic Measurements of Spontaneous Magnetic Reconnection

A new closed magnetic configuration has recently been implemented in the Versatile Toroidal Facility (VTF) utilizing internal coils to generate a poloidal field with a characteristic X-line geometry. Although driven uniformly, reconnection often occurs in short, rapid bursts triggered internally in the plasma [1]. To study in detail the onset of fast magnetic reconnection and the accompanying three- dimensional plasma dynamics, new arrays of magnetic and electrostatic probes have been constructed. These yield high- resolution profiles of the magnetic field simultaneously at several toroidal locations. Here we present preliminary measurements on the dynamical onset and evolution of fast reconnection.\\[1ex] [1] J Egedal, et al., (2007) Phys. Rev. Lett. 98, 015003.   

Experiments on the Propagation of Plasma Blobs

We investigate the large-scale motion of plasma blobs in the Versatile Toroidal Facility (VTF) using Langmuir probe arrays. Blobs, or field-aligned filaments, have been used to model plasma fluctuations in the scrape-off layer of tokamaks and other devices [1-3]. These fluctuations, which are interchange modes driven by magnetic field curvature, display a convective or `bursty' character and can sometimes form large coherent structures. We use VTF, a well-diagnosed basic plasma physics experiment, to create plasma blobs reproducibly. The experiments are designed to investigate how the average blob speed scales with various experimental parameters and to probe the internal electrostatic structure of the blobs. We find that charge exchange collisions with neutrals play a significant role in the non-linear evolution of the plasma structures. [1] Krasheninnikov S, Phys. Lett. A, 283 (2001) 368 [2] Zweben S et al, Nucl. Fusion, 44 (2004) 134 [3] Garcia O et al, Phys. Plasmas, 12 (2005) 090701   

On the filamentary structure of energetic electrons during reconnection in flares

Simulations are presented that demonstrate that magnetic reconnection in the corona does not occur as a single large-scale x-line. Rather the narrow current layers that form at x-lines form secondary magnetic islands that grow and merge to produce a turbulent bath of islands. A probability model of island growth is being developed to predict their size spectrum. A consequence of particle acceleration in any multi-island system is that energetic particles are released in narrow streams with characteristic widths controlled by the width of the dissipation region (electron skin depth) as the islands reconnect with the external macro-scale field. Thus, energetic electrons do not propagate away from the reconnection site to the solar surface as a single large-scale front but as a filamentary web. We show that the filaments of energetic particles propagate along the magnetic field as kinetic Alfven waves with propagation speeds comparable to the thermal velocity of the energetic particles. The return current therefore does not inhibit the transport of energetic particles. The kinetic Alfven wave should similarly facilitate the transport of energetic electrons to the ionosphere during substorms in the magnetosphere.   

The Onset of Fast Magnetic Reconnection is Localized

A subject of ongoing debate in the literature concerns the dependence of (fast) Hall reconnection on the system size, which is related to the issue of reconnection onset. Does the trigger occur near the boundary and propagate inward or is reconnection initiated near the X-line and propagate outward? Numerical simulations supporting either scenario exist. We present new evidence that the trigger is localized near the X-line, suggesting that local physics rather than global dynamics controls Hall reconnection. This is done by demonstrating the existence of an unstable steady-state magnetic reconnection solution which lies at the boundary of the basins of attraction of the Sweet-Parker and Hall reconnection solutions. Its identification required a novel iterative numerical technique. Eigenmodes of the unstable solution are localized near the X-line, suggesting that the onset of fast reconnection in a weakly collisional plasma initiates at the X-line. We will discuss these results in the context of other theories of fast magnetic reconnection.   

Two-scale structure of the electron dissipation region during collisionless magnetic reconnection: PIC simulations and Cluster satellite observations

Particle in cell (PIC) simulations$[1]$ and Cluster satellite observations of collisionless magnetic reconnection are presented that demonstrate that the electron dissipation region develops a distinct two-scale structure along the outflow direction. Consistent with past hybrid and two-fluid simulations, the rate of reconnection remains fast in very large systems, independent of the mass of the electrons. A surprise is the existence of an outer electron dissipation region downstream of the inner one, which extends up to 40 ion inertial lengths downstream of the X-line in the largest simulations. This outer region consists of a super-Alfvenic jet of electrons which are decoupled from the magnetic field. The existence of this outer dissipation region is confirmed by Cluster satellite observations during a current sheet crossing in the flanks of the dayside magnetopause about 30 ion inertial lengths downstream of an x-line. \newline $[1]$ Shay, M. A., J. F. Drake, and M. Swisdak, ``Two-scale structure of the electron dissipation region during collisionless magnetic reconnection,'' Submitted to Physical Review Letters, arXiv:0704.0818v1 [physics.plasm-ph]   

Asymmetric Magnetic Reconnection: General Theory and Collisional Simulations

Theories of magnetic reconnection usually assume that the plasmas on either side of the dissipation region have identical densities and magnetic field strengths. However, this canonical description is rarely realized in nature. There has been wide interest in the shock structure of fast reconnection, particularly at the dayside magnetopause, but a general theory of the structure of the dissipation region and the rate of reconnection during asymmetric reconnection has not been addressed. We derive analytical expressions from first principles using a Sweet-Parker type scaling analysis. Most of the scaling results are independent of the dissipation mechanism and, therefore, apply to asymmetric reconnection in general. Furthermore, we show that a generic feature of asymmetric reconnection is that the X-line and stagnation point are not colocated. This implies that there is a bulk flow of plasma across the X-line, as has been seen in many numerical studies and observations at the dayside. The theory is verified using two dimensional collisional magnetohydrodynamic simulations. Applications to the magnetosphere are discussed.   

Diamagnetic effects in driven magnetic reconnection

We use the two-fluid equations recently derived in [1] to study magnetic reconnection about a neutral X-point in a weakly collisional plasma, driven by external bulk flow. The equations include finite Larmor radius effects and are valid for arbitray density and temperature gradients thus accounting for complete diamagnetic effects. They also allow for strong temperature anisotropies and arbitrarily large fluctuation amplitudes, which make them appropriate for nonlinear studies. The resulting reduced model, in which the fast magnetosonic wave is suppresed, consists of seven fields: density $n$, four pressures $p_{\alpha \parallel}$, $p_{\alpha \perp}$, magnetic potential $\psi$ and electric potential $\Phi$. The evolution of the system is followed using a numerical code producing a forcing from the edge of the integration domain that starts from zero during a finite time (Taylor problem). We proceed by adding different effects gradually in order to asses the role of each one and comparing with a standard reduced model [2] without the electron inertia. The first and simplest case is for an isotropic plasma with constant temperature. Then we include finite temperature gradients and finally the effect of anisotropic pressures for both ions and electrons. [1] J.J. Ramos, Phys.\ Plasmas {\bf 14}, 052506 (2007) [2] T.J. Schep, et al., Phys.\ Plasmas {\bf 1}, 2843 (1994)   

A first-principles analytical theory for 2D magnetic reconnection in electron and Hall MHD.

While the relevance of two-fluid effects in fast magnetic reconnection is well-known,\footnote{J. Birn et al., {\em J. Geophys. Res.}, {\bf 106} (A3), pp. 3715--3719 (2001) } a first-principles theory --akin to Sweet and Parker's in resistive MHD-- has been elusive. Here, we present such a first principles steady-state theory for electron MHD,\footnote{L. Chac\'on, A. N. Simakov, A. Zocco, {\em Phys. Rev. Lett.}, submitted} and its extension to Hall.\footnote{A. N. Simakov, L. Chac\'on, in preparation} The theory discretizes the extended MHD equations at the reconnection site, leading to a set of time-dependent ODEs. Their steady-state analysis provides predictions for the scaling of relevant quantities with the dissipation coefficients (e.g, resistivity and hyper-resistivity) and other relevant parameters. In particular, we will show that EMHD admits both elongated and open-X point configurations of the reconnection region, and that the reconnection rate $E_z$ can be shown not to scale explicitly with the dissipation parameters. This analytic result confirms earlier computational work on the possibility of fast (dissipation-independent) magnetic reconnection in EMHD. We have extended the EMHD results to Hall MHD, and have found a general scaling law for the reconnection rate (and associated length scales) that bridges the gap between resistive and EMHD.   

Energetic electrons and magnetic islands during reconnection

Magnetic reconnection is widely thought to be a mechanism for electron acceleration, but exactly where and how the acceleration occurs remains an open question. Here we report case studies of magnetotail reconnection where energetic electrons and signatures of magnetic islands are observed. We found that each clearly identifiable magnetic island has a corresponding burst of energetic electrons, but strong energetic electron bursts can appear without the association with well-defined single islands. Energetic electrons are also observed at the electron current sheet, but with a much lower energy and flux that is one order of magnitude lower than those within islands. The fluxes of energetic electrons peak at sites of compressed density within magnetic islands, a feature not explained by existing theories. Strong core magnetic fields are observed within islands even for cases when the background guide field is less than 1$\%$ of the asymptotic field. The existence of strong core fields indicate that energetic electrons are either being actively produced within or introduced into the islands. because otherwise the electrons will be guided away within $\ll 1$ second. The strong density sub-structures within islands suggest that the islands may have gone through coalescence. The observation will be compared with PIC simulations of reconnection to better understand acceleration mechanisms.   

PIC simulations of core magnetic field generation in magnetic islands by reconnection

We will present results of particle-in-cell (PIC) simulations where core field generation in magnetic islands by magnetic reconnection is studied. Cluster observations reveal that multiple magnetic islands are generated by reconnection in Earth's magnetotail, and some islands have strong core fields accompanied by peaks of electron density and energetic electron flux. Using a 2D PIC simulation code, we study magnetic reconnection with multiple X-lines and magnetic islands. We will show that each X-line has a quadrupolar magnetic field due to magnetic reconnection, and at the same time, strong core fields are generated in magnetic islands even when the initial guide field is very small ($< 0.01B_0$, where $B_0$ is the asymptotic magnetic field). Some simulation results show that the peak of the core field is located at the center of each island in an early stage of the evolution of islands. As the islands evolve, the structure changes and each island has multiple peaks of core fields in a later stage. We will also study energy spectra of electrons in those islands. This research is supported by NSF, NASA, and DOE.   

Collisionless Magnetic Reconnection in Large-Scale Electron-Positron Plasmas

One of the most fundamental questions in reconnection physics is how the dynamical evolution will scale to macroscopic systems of physical relevance. This issue was recently examined for electron-positron plasmas using 2D kinetic simulations with both open and periodic boundary conditions\footnote{Daughton and Karimabadi, {\em Phys. Plasmas} {\bf 14}, 072303, 2007}. The initial phase is distinguished by the coalescence of tearing islands to larger scale while the later phase is marked by the expansion of diffusion regions into elongated current layers that are intrinsically unstable to plasmoid generation. It appears that the repeated formation and ejection of plasmoids plays a key role in controlling the average structure of a diffusion region and preventing the further elongation of the layer. Although the specific details of this evolution are affected by the boundary and initial conditions, the time averaged reconnection rate remains fast and is remarkably insensitive to the system size for sufficiently large systems. In this work, the influence of a guide field and current aligned instabilities are examined in 3D simulations. The mechanism of repeated plasmoid formation identified in 2D is also observed in these large-scale 3D simulations. This dynamic scenario offers an alternative explanation for fast reconnection in large-scale systems.   

Kinetic Theory and Simulation of Collisionless Tearing in Bifurcated Current Sheets

Bifurcated current sheets have been observed in the Earth's magnetotail and also within kinetic simulations. The development of a bifurcated current layer may be the direct result of magnetic reconnection or may be due to the nonlinear evolution of the lower-hybrid drift instability. Although the equilibrium theory of these structures has been considered by a number of researchers, the linear stability has not been rigorously treated. In this work, a Vlasov equilibrium is constructed that permits both the current bifurcation and temperature anisotropy to be independently adjusted. The linear theory for colllisionless tearing is performed using standard techniques and compared against a formally exact numerical treatment. The resulting dispersion relation and mode structure are verified with fully kinetic particle-in-cell simulations. While temperature anisotropy \(T_{\perp} > T_{\parallel}\) is always strongly destabilizing, the bifurcated current profile enters as a stabilizing influence on the tearing mode. A simplified analytic theory is reasonably accurate for long wavelength modes, but the short wavelength regime requires the full numerical treatment to accurately compute the growth rate.   

The Influence of Sheared Parallel Flows on Collisionless Magnetic Reconnection

The first results of an ongoing study of the influence of sheared parallel flows on collisionless magnetic reconnection are presented. In particular, we focus on the linear stability of a newly developed exact kinetic equilibrium which incorporates sheared parallel flows into the well-known Harris current sheet configuration. Using a variety of tools including analytical theory, numerical solution of the complete linearized Vlasov-Maxwell system, and fully kinetic 2D PIC simulations, we demonstrate that the stability properties of a thin current sheet in the presence of significant (of the order of ion thermal speed) flows differ significantly from those predicted by MHD analysis. Large flow shear is typically found to have a stabilizing influence on the reconnecting mode, while the shear-driven instability, which has been proposed as the mechanism responsible for the onset of reconnection, is either completely stable, or has growth rate that is dramatically lower than that predicted by MHD analysis. Preliminary results from nonlinear PIC simulations indicate that the onset of fast reconnection proceeds in a manner that is similar to that in the absence of the flow. None of the simulations exhibit highly wrapped vortices typically produced by MHD simulations of similar configurations.   

Forced Magnetic Reconnection with Open Boundary Conditions

We present kinetic simulations of collisionless forced magnetic reconnection driven by different models of magnetic flux inflows, with open boundary conditions applied in the outflow directions. We use the implicit Particle-in-Cell code CELESTE3D [1], which retains kinetic effects for both electrons and ions. Different from results of fluid simulations, the reconnection rate is intermittent rather than steady even when the driving inflow is constant. Similar to the pervious discoveries by W. Daughton \textit{et al.} [2], we find secondary islands grow as the electron diffusion region is elongated over time. For the well-studied Newton Challenge reconnection problem, compared to results with periodic boundary conditions, here we find that with the open boundaries, at the same driving amplitude, fast reconnection starts earlier and reaches a bigger maximum reconnection rate. We will study the dependence of the maximum reconnection rate on the driving amplitude and other factors. References: [1] G. Lapenta, J. U. Brackbill, and P. Ricci, Phys. Plasmas \textbf{13}, 055904 (2006) [2] W. Daughton, J. Scudder and H. Karimabadi, Phys. Plasmas \textbf{13}, 072101 (2006)   

Micro-reconnection at the $c/\omega_{pe}$ Scale Length$^*$

A phase space (non-fluid) approach is needed to describe modes that perturb the magnetic field in a sheared field geometry, lead to the formation of strings of magnetic islands, and have transverse scale distances that are of the order of $c/\omega_ {pe}$. The driving factor is the transverse electron temperature gradient. The plasma density gradient has a strong influence and is shown to reduce the mode frequency considerably relative to its upper bound $k_{\perp}c |dT_ {e}/dr|/( eB )$. The mode characteristics are intrinsically different from the commonly known electrostatic ETG modes, that do not produce magnetic islands and have shorter wavelengths. The effect of the present modes is to decrease the anisotropy of the electron thermal conductivities by increasing the ratio of $D^{th}_ {\perp e}/D^{th}_{\| e}$ relative to its very small classical value. In particular $D^{th}_{\perp e}$ is estimated as $\alpha_{D}(c/\omega_{pe}) c | dT_{e}/dr | /(eB)$ where ${\alpha}_{D}$ is a finite numerical coefficient. The theory of mesoscopic reconnecting modes (so-called drift-tearing) that can produce macroscopic magnetic islands depends heavily\footnote{B. Coppi in ``Collective Processes in Macroscopic Systems'' Eds. G. Bertin \textit{et al}., Publ. \textit{World Scientific} (2007) and MIT-LNS Report 06/11 (2006).} on the finiteness of $D^{th}_{\perp e}/D^{th}_{\| e}$ besides that of electrical resistivity. Therefore it has been assumed that these mesoscopic modes develop$^1$ from a background of micro-reconnecting modes of the kind we have described. $^*$Sponsored in part by the US D.O.E.\vspace{-0.1in}   

Roles of Magnetic Reconnection and Developments of Modern Theory$^*$

The role of reconnection was recognized in Solar and Space Physics and auroral substorms were suggested to originate in the night-side of the Earth's magnetosphere as a result collisionless reconnection\footnote{B. Coppi, \textit{Nature} \textbf{205}, 998 (1965).} well before the kind of modern theory employed for this became applied to laboratory plasmas. Experiments have reached low collisionality regimes where, like in space plasmas, the features of the electron distribution and in particular of the electron temperature gradient become important and the factors contributing to the electron thermal energy balance equation (transverse thermal and longitudinal diffusivities, or electron Landau damping\footnote{B. Coppi, J.W.-K. Mark, L. Sugiyama, G. Bertin, \textit{Phys. Rev. Letters} \textbf {42}, 1058 (1978) and J. Drake, \textit{et al}., \textit{Phys. Fluids} \textbf{26}, 2509 (1983).} play a key role. For this an asymptotic theory of modes producing macroscopic islands has been developed involving 3 regions, the innermost one related to finite resistivity and the intermediate one to the finite ratio of the to thermal conductivities\footnote{B. Coppi, C. Crabtree, and V. Roytershteyn contribution to Paper TH/R2$-$19, I.A.E.A. Conference 2006.},$^4$. A background of excited micro-reconnecting modes, driven by the electron temperature gradient, is considered to make this ratio significant\footnote{B. Coppi, in\textit {``Collective Phenomena in Macroscopic Systems''} Eds. G. Bertin \textit{et al.} (World Scientific, 2007) MIT-LNS Report 06/11(2006).} $^*$Supported in part by the US D.O.E.   

Overview of recent results from the Columbia Non-neutral Torus and future plans

The Columbia Non-neutral Torus (CNT) is a compact, two-period stellarator created from four circular coils, dedicated to the study of non-neutral and electron-positron plasmas on magnetic surfaces. First results include the confirmation that pure electron plasmas can be confined stably in a stellarator, with confinement times of up to 20 msec. Transport is driven by the perturbing presence of internal rods, as well as by electron-neutral collisions. CNT has started operating with a retractable emitter allowing operation without internal rods, eliminating this source of transport. Reducing the neutral driven transport by reducing the neutral pressure to less than $2\times 10^{-10}$ Torr, a confinement time exceeding 1 second is predicted. Despite the long confinement times, the collisional transport rate is much higher than expected from neoclassical predictions. In fact, confinement times are on the order of the electron-neutral collision time, possibly caused by bad orbits despite the large radial electric field. This poster will give an overview of recent CNT results and future plans.   

Confinement of pure electron plasmas in the Columbia Non-neutral Torus

One goal of the Columbia Non-neutral Torus (CNT) research program is to investigate the possibility of enhanced confinement in stellarators due to high electric fields. Non-neutral plasmas with high electric fields are predicted to have long confinement times. Measured confinement times have fallen somewhat short of these predictions, however. There are several factors influencing the transport in these plasmas, including the presence of insulated rods, the neutral pressure, the ion fraction (through ion-driven instabilities), the match of equipotential and magnetic surfaces, and possibly prompt losses due to bad orbits. Each of these factors has been or is presently being investigated in CNT. Results are presented from the theoretical scaling of the neoclassical confinement time, and the measured confinement time's dependence on the presence of rods and on the neutral pressure. Comparisons are made between the predicted and measured values and possible explanations for the discrepancy are offered. Calculations and measurements of the ion fraction in these plasmas are also presented.   

Observations of an Ion Driven Instability in Non-neutral Plasmas Confined on Magnetic Surfaces.

The Columbia Non-neutral Torus (CNT) is a stellarator designed to confine non-neutral plasmas, including non-neutral ion-electron plasmas. When the ion density exceeds approximately 10{\%} of the electron density in CNT, an instability is observed. The instability has a poloidal mode number of m = 1, despite the fact that CNT does not contain an m = 1 rational surface. The measured frequency of the instability decreases with increasing magnetic field strength, and increases with increasing radial electric field, suggesting that the instability is linked to the ExB flow of the plasma. The frequency does not, however, scale exactly as E/B, and it depends on the ion species that is introduced. These observations, along with the measured m = 1 poloidal mode number imply that the instability involves an interaction between ions, and electrons that are mirror trapped and therefore do not circulate toroidally. Results from a numerical code which follows the complex (and sometimes chaotic) motion of an ion in CNT are also presented.   

Pure Electron Equilibrium and Transport Jumps in the Columbia Nonneutral Torus

The Columbia Non-neutral Torus (CNT) is a simple stellarator, which is being used to study electron rich plasmas. At very low neutral pressures the plasmas are pure electron plasmas. The equilibrium depends on electrostatic and transport effects.The dependence of the equilibrium on the characteristics of the electron source have been studied. The plasma may be created by a single negatively biased filament either on or off the magnetic axis, or by multiple filaments. The toroidal location of the emitter has also been varied. Because of the large toroidal variations of the magnetic field strength in CNT the toroidal location affects the ratio of passing versus trapped particles, which affects transport. For an emitting filament within the plasma the loss rate of electrons from the plasma is the same as the emission current. As parameters that increase transport are varied abrupt jumps in emission current occur. These jumps imply discontinuous changes in the confinement time. The jumps occur at specific values of the emission current, i.e. at specific transport rates. Other parameters that affect transport, such as neutral pressure and magnetic field strength, only affect the jumps to the extent that they affect transport. The jumps show hysteretic behavior indicative of regions in the current-voltage characteristic of the plasma-diode system with negative differential resistance.   

Installation and Operation of a Conducting Boundary in the Columbia Non-Neutral Torus

The Columbia Non-Neutral Torus (CNT) is a compact stellarator, which is currently being used to study non-neutral plasmas confined on magnetic surfaces. Previously, confinement times up to 20 ms have been measured, limited in part by enhanced transport caused by potential variation along magnetic surfaces. Conducting meshes that conform to the last closed magnetic surface were recently installed in CNT. These meshes create an equipotential boundary at the last closed surface, improving the match between equipotential and magnetic surfaces as well as offering new non-intrusive methods to diagnose the plasma. The conducting mesh boundary is composed of 13 individual sectors that can act as probes. These probes can measure the decay of an induced image charge, plasma oscillations, or actively drive oscillations to diagnose the plasma properties. A description of the apparatus and the results of initial experiments are presented. A limiter probe surrounding the majority of a cross section has also been inserted to directly measure confinement by the decay of electron flux. Experiments have been completed demonstrating that electron flux to a point probe at the last closed flux surface accounts for less than 10 percent of all the electrons leaving the magnetic surfaces. These results and their implications for a limiter probe diagnostic will be discussed.   

Numerical Studies of Transport in the Columbia Non-Neutral Torus

The confinement of pure electron plasmas in the Columbia Non-neutral Torus (CNT) stellarator is limited by the presence of internal probes and electron-neutral collisions. The probes can be removed, so the transport of fundamental interest is the neoclassical transport associated with the electron-neutral collisions. This transport depends on the distance the electron trajectories deviate from the magnetic surfaces. The magnetic fields in CNT have not been optimized to minimize the deviation of trajectories from the surfaces. The reason is the electric potential is very large compared to the temperature, and the $E\times B$ drift dominates the magnetic drifts. In particular, the variation in the electric potential across the magnetic surfaces greatly reduces the radial drift of the electrons. However, unlike the situation in a quasi-neutral plasma, the electric potential also varies within the surfaces, which adds to the complexity of the trajectories and can increase the radial drifts. We have written a code using magnetic coordinates to integrate the electron drift trajectories in the electric and magnetic fields expected in CNT equilibria. A Monte-Carlo code including both electron-electron collisions and electron-neutral collisions will be used to determine if the plasma transport in CNT is neoclassical, how it depends on the electron density and how it is affected by the potential not being a function of flux only.   

Confinement Time Exceeding One Second in a Toroidal Electron Plasma

Pure electron plasmas ($n=2\times 10^7$ cm$^{-3}$, $a=1.27$ cm, $R_p=17.4$ cm) are confined for times exceeding one second in a new toroidal device, the Lawrence Non-neutral Torus II. The plasma is trapped in a 270$^{\circ}$ toroidal arc by application of gate potentials to sections of a sectored gold-plated toroidal boundary ($b=3.81$ cm, $R_0=18$ cm). At base vacuum pressures below $10^{-8}$ torr and magnetic field strengths approaching 700 gauss, the $m=1$ diocotron mode is excited by applying several cycles of rf near the resonant frequency to a section of the wall. The $m=1$ frequency, which is approximately proportional to the trapped charge, decays on a three second timescale, a confinement time that exceeds by at least an order of magnitude the confinement observed in all other toroidal traps for non-neutral plasmas. Numerical simulations that include toroidal effects are employed to accurately extract plasma charge and $m=1$ mode amplitude from the experimental data. Future work will include attempts to withdraw the electron source in order to study confinement in a full torus. This work is supported DOE-NSF Grant 0317412.   

Magnetic Field Dependence of the Diffusion Coefficient in Asymmetry-Induced Transport

The dependence of the asymmetry-induced radial particle flux $\Gamma$ on axial magnetic field $B$ is complicated by the fact that the field enters the physics in at least two places: in the asymmetry-induced first order radial drift velocity $v_r=E_ {\theta}/B$ and in the zeroth order azimuthal drift velocity $v_ {\theta}=E_{r}/B$. To separate these, we assume the latter always enters the physics in the combination $\omega -l\omega_R$ where $\omega_R(r)=v_{\theta}/r$ is the column rotation frequency and $\omega$ and $l$ are the asymmetry frequency and azimuthal mode number, respectively. We then select from a $\Gamma$ vs $r$ vs $\omega$ data set those points where $\omega- l\omega_R=0$, thus insuring that any function of this combination is constant. When the selected flux is plotted versus the density gradient $\nabla n$, a roughly linear dependence is observed, showing that our assumption is valid and that we have isolated the diffusive contribution to the transport. The slope of a least-squares fitted line then gives the diffusion coefficient $D$. Varying the magnetic field, we find $D\propto B^{-1.33\pm 0.12}$. This does not match the scaling predicted by resonant particle transport theory\footnote {D.L. Eggleston and T.M. O'Neil, Phys. Plasmas 6, 2699 (1999).}.   

Limits of Particle-beam Extraction from Single-Component Plasmas

Recently, a non-destructive technique was developed to create finely focused beams of electrons (or positrons) from single-component plasmas confined in a Penning-Malmberg trap\footnote{J. R. Danielson et al., Appl. Phys. Lett. {\bf 90}, 081503 (2007).}. This technique exploits the fact that the plasma potential is largest near the plasma center; thus, when the confining potential at one end is carefully lowered, a beam is formed that is composed only of particles escaping from the region near r = 0. Here, we investigate the limits of this technique. A simple model for beam extraction is described that predicts a Gaussian beam profile when the number of extracted particles is small. This expression gives a minimum beam diameter of four Debye lengths (full width to 1/e) and is verified using electron plasmas over a broad range of plasma temperatures (0.05 $< T <$ 2 eV) and densities (0.06 $< n <$ 2$\times$10$^{10}$). Numerical calculations are used to predict the profiles of beams with large numbers of extracted particles, and they are in fair agreement with the measurements. The extraction of over 50\% of a trapped plasma in a train of nearly identical beams is demonstrated. Applications to create state-of-the-art positron beams, including the possibility of extracting the beam from the magnetic field to form an electrostatic beam, are also discussed.   

Attracting Fixed Points for Radially Compressed Single-Component Plasmas

Rotating electric fields are used to compress electron plasmas confined in a Penning-Malmberg trap using the so-called rotating wall (RW) technique\footnote{J. R. Danielson and C. M. Surko, Phys. Rev. Lett. {\bf 95}, 035001 (2005); and Phys. Plasmas {\bf 13}, 055706 (2006).}. Over a broad range in RW frequency, plasmas can be compressed until the $E \times B$ rotation frequency, $\omega_{\rm E}$ (with $\omega_{\rm E}$ $\propto n$, the plasma density), approaches the applied frequency, $\omega_{\rm RW}$. Bifurcation and hysteresis are observed between low-density and high-density steady states as a function of the applied RW electric field amplitude and frequency. Here, models of the drive and drag torques are used to describe the stable, attracting fixed points of the system. Key ingredients are a drag torque due to a plasma-mode resonance, driven by static trap asymmetries, and a RW drive torque that passes rapidly through zero as $\omega_{\rm E}$ approaches $\omega_{\rm RW}$. A number of tests of the model are described, including perturbation experiments to confirm the nature of the RW torque and to measure its magnitude near the high-density fixed point. Open questions for future research, including a possible thermodynamic model to describe the plasma dynamics, are discussed.   

A Multicell Trap for Positron Storage

We describe several techniques necessary for the practical implementation of a multicell Penning-Malmberg trap\footnote{J. R. Danielson {\it et al.}, Phys. Plasmas {\bf 13}, 123502 (2007).}$^,$\footnote{C. M. Surko {\it et al.}, Rad. Phys. Chem. {\bf 68}, 419 (2003).} designed to increase positron storage by orders of magnitude (e.g., to particle numbers N $\geq 10^{12}$). Experiments are done using test electron plasmas. A technique is described to move plasmas across the confining magnetic field and dump them at specific radial and azimuthal locations. Techniques are deomonstrated to fill and operate two in-line plasma cells simultaneously and to use 1 kV confinement potentials to trap 3$\times$10$^{10}$ particles. These experiments establish the capability to create, confine, and manipulate plasmas with the parameters required for a multicell trap, namely N $\geq$ $10^{10}$ in a single cell with temperatures $\leq$ 0.2 eV, plasma lengths $\sim$ 10 cm, and radii $\sim$ 0.2 cm. The design of a new structure to test the confinement of plasmas in off-axis cells is presented, as well as an improved design for a multicell positron trap for $10^{12}$ particles. Potential applications, including prospects for a portable positron trap (i.e., to replace conventional isotope and accelerator-based sources) will also be discussed.   

SSPX Achievements and Future Directions for Spheromak Research

The Sustained Spheromak Physics Experiment (SSPX) has achieved significant results including peak electron temperature T$_{e} \quad >$ 500eV, magnetic field B $>$ 1T, plasma current I$_{p}\sim $1MA, and core electron thermal diffusivity $\chi _{e}<$ 10 m$^{2}$/sec. Several new operating regimes have demonstrated more efficient building and sustaining of self-organized spheromak magnetic fields. A vigorous collaborative campaign to develop new capabilities for the NIMROD 3D resistive MHD code and benchmark against SSPX data has improved physics understanding and predictive capability. Recent results indicate neutral beam injection is an important next step for evaluating energy confinement and exploring NBI current drive as a means of dynamo-free sustainment. Goals identified for next-generation spheromaks include longer pulses, higher flux amplification through variable bias flux operation, and thinner walls with active feedback control of external tilt/shift modes. Work performed under the auspices of the US DOE by UC-LLNL under contract W-7405-ENG-48.   

Magnetic Field Build-up in SSPX

Magnetic field build up experiments in SSPX using the modular capacitor bank have produced discharges (extended formation) with the highest edge poloidal fields and multi-pulse discharges that continue to build magnetic field in a stepwise manner. The ratio of B$_{p}$/I$_{gun}$ for the multi-pulse discharges ($\sim $0.9T/MA) exceeds the value of B$_{p}$/I$_{gun}$=0.65T/MA obtained with a standard discharge (fast formation followed by sustainment discharge). As suggested by simulations, the higher ratio with the new injected current waveforms may reflect the longer total formation pulse duration (building to higher field due to the longer current pulse) than previous discharges. Recent results from multi-pulse and extended formation experiments and near mega-ampere injected current discharges will be presented.   

Electron Temperature Measurements and Energy Transport in SSPX

Time-resolved measurements (\underline {$<$}100 $\mu $s) have been made with a multi-pulse Thomson scattering diagnostic in the SSPX spheromak experiment, to obtain radial electron density and temperature profile during plasma formation and sustainment. In most discharges three regimes are observed with respect to T$_{e}$ and n$_{e}$ evolution. Initially there is a cold ($<$100 eV) formation phase, followed by a hollow T$_{e}$ profile with maximum temperatures 100-200 eV, and a final heat-up and cool-down phase where we obtain the highest plasma temperatures (350+ eV). The transition from hollow to peaked T$_{e}$ is quite sharp ($\sim $50 $\mu $s) and the recent upgrade to double-pulse Thomson scattering ($\sim $40 $\mu $s between pulses) facilitates capturing this transition. We also present simulations using the CORSICA code where the equilibrium is kept fixed and the discharge is evolved to observe the change in temperature profiles for different transport coefficients. In addition, electron transport and heating will be correlated with measured MHD mode activity. Temperature and density measurements during multi-pulse coaxial gun-current operation will also be presented. * Work performed under the auspices of the US DOE by University of California Lawrence Livermore National Laboratory under contract W--7405--ENG--48.   

Predictive capability for whole-device spheromak MHD physics

Resistive, single-fluid (NIMROD) MHD simulations reproduce many SSPX results and contribute to our understanding of spheromak physics. Simulation is benchmarked to experiment including sensitivity to simulation parameters: viscosity, maximum toroidal mode number, finite-element number, density, and particle diffusivity. Quantities comparing well with experiment include gun voltage, thresholds for spheromak formation and sustainment, and magnetic field strength and time evolution. MHD mode amplitudes and q-profiles are moderately sensitive. Precise time histories, e.g., the rate of reconnection events, are more sensitive but have little effect on average quantities, e.g. magnetic field strength. Experimental Te is 20-50{\%} higher than simulations -- flux surface quality is very sensitive to small changes in mode activity. The results provide confidence in simulations of upgrades or advanced spheromak experiments. Refs.: C.R. Sovinec, et al., Phys. Rev. Lett. \textbf{94}, 035003 (2005); B.I. Cohen, et al., Phys. Plas. \textbf{12}, 056106 (2005); E.B. Hooper et al., Phys Plas. \textbf{12}, 092503 (2005); E.B. Hooper, et al., Nucl. Fusion (in press).   

Linear MHD Stability Analysis of the SSPX Spheromak

Good correlation between the toroidal mode numbers of measured magnetic fluctuations in high temperature SSPX plasmas and presence of low-order rational surfaces in the reconstructed q profiles, suggests that the quality of magnetic surfaces in SSPX is sufficiently good for applying standard linear MHD stability analyses. Previously we have reported on benchmarking the code NIMROD against GATO, with good agreement in growth rates for ideal-MHD internal kinks and an external kinks with no current on open field lines (for equilibria imported from the code Corsica). Recent stability analyses also show that presence of low order rational surfaces causes internal modes to become unstable. We will report on the progress in applying these tools for assessing beta limits in SSPX, using NIMROD analyses including current on open field lines and for comparison with experiments.   

Neutral Beam Current Drive in Spheromak plasma and plasma stability

A key question for the Sustained Spheromak Physics Experiment (SSPX) is understanding how spheromaks can be sustained by other current drive tools such as neutral beam current drive. Another question is whether the present relationship between current and maximum spheromak magnetic field (plasma beta) is related to Alcator-like ohmic confinement limit or is a stability limit. Using the code CORSICA, the fraction of neutral beam current drive that can be achieved has been calculated for different injection angles with a fixed equilibrium. It is seen that relaxing the equilibrium with this drive simply drives the core safety factor to low values. Other equilibria where the NBI may give aligned current drive are being explored. Free-boundary equilibria calculations are underway to see what hyper-resistivity model gives the observed sustained SSPX performance and include that in the NBI calculations. Work performed under the auspices of the US DOE by University of California Lawrence Livermore National Laboratory under contract W-7405-ENG-48.   

Flux amplification in SSPX

Flux amplification---the ratio of poloidal flux enclosed between the magnetic and geometric axes to that between the separatrix and the geometric axis---is a key measure of efficiency for edge-current-driven spheromaks. With the new, modular capacitor bank, permitting flexible programming of the gun current, studies of flux amplification under various drive scenarios can be performed. Analysis of recent results of pulsed operation with the new bank finds an efficiency $\sim $ 0.2, in selected shots, of the conversion of gun energy to confined magnetic energy during the pulses, and suggests a route toward sustained efficiency at 0.2. Results of experiments, a model calculation of field build-up, and NIMROD simulations exploring this newly suggested scenario will be presented.   

Measurements of spheromak formation and field buildup at SSPX using a double magnetic probe array

A specially designed magnetic probe consisting of two linear arrays that measure Bx, By, and Bz, is being used to investigate magnetic evolution during spheromak formation, and during multiple gun current pulses on top of a baseline current at SSPX. The measurements reveal that at the start of each pulse there is a time lag in the magnetic response of the closed flux region, while the open flux (intercepting the gun electrodes) responds immediately. This is interpreted as the time to build enough helicity on the open flux, before reconnecting and adding flux to the closed surfaces. Magnetic reconstructions after pulsed buildup using CORSICA show good agreement with the data. A code that simulates the magnetic field from current-carrying flux ropes is used to reproduce the field measured during flux buildup. The code includes an optimization routine that finds the rope shape that best fits the data in order to estimate helicity in the open flux. Work performed under the auspices of the US DOE by University of California Lawrence Livermore National Laboratory under contract W-7405-ENG-48.   

Stereo Imaging as a Diagnostic in SSPX

A stereoscopic imaging diagnostic to provide three-dimensional information of plasma behavior during spheromak formation is being designed and constructed at SSPX. The diagnostic consists of two convex mirrors, macor/stainless steel mounts, a high-speed camera and a telephoto lens. Using a titanium adhesion layer, a thin gold layer is applied to a stock lens providing greater than 95 percent reflectivity at 650nm and a wide field of view. The mirrors and mounts will be under vacuum while the camera and telephoto lens will be located outside the spheromak chamber. The high-speed camera will view both mirrors in the vacuum chamber and provide two images per plasma shot. Each image will be divided such that each mirror will comprise one image. Software will be used to overlay the images to provide a three-dimensional effect. The depth of objects inside the flux conserver can be found as a function of the overlap of the two images. Work performed under the auspices of the US DOE by University of California Lawrence Livermore National Laboratory under contract W-7405-ENG-48.   

Ion Doppler Spectroscopy Measurements on SSPX

The Sustained Spheromak Physics experiment (SSPX) at Lawrence Livermore National Laboratory is performing experiments pertaining to formation and sustainment of spheromak plasmas. An existing high resolution Ion Doppler Spectrometer (IDS) has been reactivated to measure impurity ion temperature and velocity. The IDS is composed of an Instruments S.A. HR 1000 Czerny-Turner monochromator with diffraction grating line density of 2400 lines/mm, which allows for first order spectra between 300 and 600nm. Combined with a 16 channel photomultiplier tube assembly in place of the output slit, a spectral width of 5 nm over 16 individual time-resolved spectra is achieved. By observing the Doppler broadening and shifting of OIII and OIV lines in the plasma, time resolved ion temperature and flow information can be investigated. As an added check, a separate Ocean Optics HR4000 spectrometer is used to obtain a time-integrated spectrum of each shot, in order to verify the presence of oxygen line radiation. Work performed under the auspices of the US DOE by University of California Lawrence Livermore National Laboratory under contract W--7405--ENG--48.   

EUV spectroscopy on the SSPX spheromak

EUV plasma spectroscopy is one of the diagnostics used at the Sustained Spheromak Physics Experiment (SSPX) to study plasma impurity ions. SSPX produces hydrogen plasmas of densities around 10$^{14}$ cm$^{-3}$ with peak electron temperatures from 10 eV up to 550 eV, thus covering a broad range of plasma conditions. The diagnostic consists of a grating spectrometer with a field of view through the magnetic axis at the mid-plane of the spheromak. It employs a spherical flat-field grating, covering the spectral region of 25 -- 400 {\AA} with a resolution of 1 {\AA}. The recording of spectra is done using a Photometrics CCD camera. Several charge states of low-Z elements have been identified, notably B, C, N and O. Of the heavier elements, Cu and Ti are found in the machine, again in a variety of charge states. We are exploring the possibility of injecting metallic compounds, such as tungsten and iron, of interest to fusion engineering, atomic theory and atomic astrophysics. Work at UC Lawrence Livermore National Laboratory was performed under the auspices of the US Department of Energy under Contract No W-7405-ENG-48.   

Correlation between gun current and ion temperature in SSPX plasma

SSPX diagnostics include ion temperature, Ti, from a Compact Neutral Particle Analyzer, electron temperature, Te, from Profile Thomson Scattering and time resolved soft X-ray ratios, and electron density, ne, from CO2 laser interferometry. We examine the correlations between these parameters and the SSPX gun current, in shots with multiple pulses of helicity injection. The measurements show that any increase in the gun current in an individual shot coincides with an increase in the ion temperature and a decrease in electron temperature and density. We also notice that an increase of helicity injection from shot to shot seems not to affect the ion temperature but influences greatly the neutral flux. This may be due to high gun current, which opens the field lines allowing more ions to escape confinement and then migrate to edge where they can interact with the neutrals. Work supported under the auspices of the US DOE by UCLLNL under contract W-7405-ENG-48.   

Correlations of Turbulent Magnetic Field Parameters with Electron and Ion Temperature Measurements in SSPX Plasmas

A new approach to turbulence physics provides a new context for turbulent diagnostic parameters in SSPX magnetic field fluctuations. Using the diagnostics for: ion temperature, Ti, from a Compact Neutral Particle Analyzer; electron temperature, Te, from Profile Thomson Scattering and time resolved soft X-ray ratios; and electron density, ne, from CO2 laser interferometry, we can now study the impact of variations in the SSPX helicity injection during a single shot on magnetic field fluctuations. We will report on changes in the complexity, changes in the rate of energy transfer through the various lengths scales, changes in characterizing fluctuation frequencies along with changes in the turbulent energy in the magnetic field fluctuations for a variety of shots with special attention on the relationships between these changes and the helicity, electron temperature and ion temperature determinations.   

Correlation of Soft X-ray Emission with Thompson Scattering Measurements of Electron Temperature in SSPX

In an effort to measure time-resolved changes in the plasma temperature over the 100 -- 300 eV range, soft X-ray photodiodes have been installed in SSPX. Two sensors with different quantum efficiency versus frequency distributions are aligned along a common chord tangent to the magnetic axis of the plasma. Analysis of the ratio of the two signals offers time-resolved insight into Bremsstrahlung soft X-ray emissions, which are a function of the chord integrated electron temperature. Results of a numerical model for the soft X-ray ratio are compared to experimental measurements. Correlation of the temperature data from these sensors to the diagnostic data taken from a Thomson scattering apparatus will be presented.   

Overview of results from the Caltech Spheromak Formation, Astrophysical Jet, and Solar Coronal Loop Simulation Experiments

These experiments involve magnetized plasma guns with (i) coaxial symmetry (spheromak formation studies, astrophysical jet simulation) and (ii) bipole symmetry (coronal loop simulation experiment). Both experiments form MHD jets that fill magnetic flux tubes linking the electrodes with plasma ingested from sources at the electrodes. Diagnostics include high-speed photography, HeNe interferometry, optical spectroscopy (Stark broadening density, Doppler velocity, line ratio temperature), color-coded imaging of different gases, and magnetic probes. The observed flux tubes are bright, dynamic, plasma-filled, and collimated. Collimation is interpreted as due to a shock-like pile-up of azimuthal magnetic flux frozen into the current-carrying jet. Observations include (i) dependence of jet velocity on electric current, (ii) what happens when a jet impacts a gas target, (iii) spatial dependence of jet velocity and density, (iv) a non-MHD particle orbit instability. Jet ingestion of plasma has been vividly imaged using different gases on the cathode and anode of the coronal loop experiment.   

Plasma tubes becoming collimated as a result of MHD pumping

Long collimated magnetized plasma tubes commonly occur in nature, ranging from solar coronal loops ($10^{7\mbox{--}8}$~m) to astrophysical jets ($10^{15\mbox{--}22}$~m). Plasma jets produced by the Caltech planar spheromak gun develop structures bearing a striking resemblance to these natural plasma tubes. We report detailed new experimental measurements$^{\dagger}$ of gun-produced plasma jets that support a recently-proposed MHD pumping model$^{\ddagger}$ as a universal collimation mechanism. Time- and space-resolved spectroscopic measurements show (i) suprathermal flow (30--50~km/s), (ii) large density amplification from $10^{17}$ to $10^{22\mbox{--}23}$~m$^{-3}$ in an Alfv{\'e}nic time scale, and (iii) flow slowing down and mass accumulation at the jet front. High-speed camera imaging shows that the collimation occurs at the jet front. These observations are consistent with the MHD pumping model which predicts (i) magnetic pumping of plasma particles from a high-density source region into a flux tube and (ii) tube collimation if the flow slows down leading to accumulation of mass and thus concentrating the azimuthal magnetic flux frozen in the mass flow (i.e., increasing the pinch force). $^{\dagger}$G. S. Yun, PhD thesis (2007) $^{\ddagger}$P. M. Bellan, Phys. Plasmas 10(2), 1999 (2003).   

Flow velocity measurements and X-ray imaging of merging flux tubes

At the Caltech Spheromak Experiment, eight different flux tubes merge to form a collimated axially symmetric plasma jet. The plasma flow velocity in the collimated jet was calculated using the time of flight measurement from the density trace of a heterodyne He-Ne interferometer$^*$. The velocity directly correlates with the toroidal magnetic field created by the axial plasma current through the jet. The plasma jet ingests magnetic helicity and energy into bulk plasma. A longer plasma jet has a larger inductance as it links more flux across itself. Since magnetic energy scales linearly with the plasma inductance, a faster plasma jet is expected to have higher magnetic energy. An energy analysis of the plasma jet is currently underway. The analysis should be applicable to other axially symmetric plasma experiments as well. Magnetic reconnection drives the merging process of the individual flux tubes into the single jet. In the experiment, reconnection is also concurrent with X-ray emission in the EUV/soft X-ray band. A high speed X-ray imaging system is being developed (exposure time $10-300$ ns) for imaging the plasma in the EUV band. The small exposure time is expected to give insights into the fast plasma dynamics during the merging of flux tubes. \newline $^*$D. Kumar, P. M. Bellan, Rev. Sci. Instrum. 77, 083503 (2006)   

Overview of the Helicity Injected Torus Program

The Helicity Injected Torus with Steady Inductive Helicity Injection (HIT-SI) spheromak experiment [Jarboe, Fus.Tech., v.36, p.85 (1999)] addresses critical research areas for spheromak formation and sustainment, including current drive, high-beta operation, confinement quality, and efficient steady-state operation. HIT-SI has a ``bow-tie'' shaped, axisymmetric confinement region with a major radius of 0.33 m, and an axial extent of 0.57 m. Attached to the confinement region are two half-torus helicity injectors, one mounted on each end of the flux conserver. HIT-SI has produced up to 30 kA of toroidal current in spheromaks generated using less than 4 MW of applied power, demonstrating that Steady Inductive Helicity Injection can create and sustain discharges with modest power requirements. HIT-SI has recently been repaired and upgraded, with an improved flux conserver, higher helicity and power injection, better diagnostic coverage, and an improved plasma-facing insulating surface. HIT-SI operational and diagnostic improvements, and corresponding physics studies, will be summarized.   

The physics of steady-state CHI in an ST

The HIT-II spherical tokamak (major radius 0.30 m, minor radius 0.20 m) is capable of using Coaxial Helicity Injection (CHI) to form and sustain low-aspect-ratio axisymmetric discharges. The physics of CHI-driven HIT-II discharges is now fairly well understood, with intuitively derived models and scalings matching the entire HIT-II experimental database. These physics results include: (1) open-flux CHI discharges are current sheets attached to the electrodes, and the sheet thickness is proportional to the inter-electrode distance; (2) the injector current and open-flux toroidal current match the models, including the independence of open-flux current Ip from the TF coil current; (3) thin-sheet CHI discharges can exhibit poloidal flux amplification and buildup of toroidal current beyond the open-flux results; (4) the mechanism for poloidal flux amplification is injector-based reconnection activity (not a coherent mode in the confinement region) requiring a minimum rotation of the magnetic field in the injector region; and (5) flux-amplification discharges exhibit features of a confined plasma core. Flux-amplification discharges in HIT-II are strongly paramagnetic, have total Ip as high as 350 kA, and exhibit flux amplification in both low-TF and high-TF regimes. These physical results will be explained in detail, as well as the key parameters, scalings, and thresholds.   

Evidence of closed flux during CHI formation of a spherical tokamak in the HIT-II experiment

The Helicity Injected Torus - II (HIT-II) experiment has demonstrated current drive by transformer action (OH), Coaxial Helicity Injection (CHI) and combinations of both. The electron temperature and density profiles of plasmas in HIT-II are measured by multi-point Thomson scattering (MPTS), and magnetic equilibria are reconstructed with EFIT. Internal probing of relaxed CHI discharges shows significant poloidal flux amplification. EFIT reconstructions of relaxed CHI discharges indicate significant closed flux, and poloidal flux increase in time. CHI initiated OH plasmas generate closed flux during the purely CHI startup. Temperature profiles of purely CHI plasmas do not match open flux models. When CHI is added to an ohmic plasma, the edge temperature drops by 75\%, and the edge density doubles, while the core plasma properties remain similar to OH only discharges, indicating a transport barrier. The simplest explanation of the data is the formation and sustainment of closed flux during CHI current drive. The limitations on HIT-II CHI discharges are discussed, suggesting refinements to future experiments.   

Nimrod Simulations of Decaying and Driven HIT-SI Plasmas

The Steady Inductive Helicity Injected Torus (HIT-SI) is a spheromak that uses two semi-toroidal injectors to provide steady inductive helicity injection (SIHI), which produces and sustains a spheromak with significant toroidal current by generating poloidal flux using relaxation current drive. NIMROD's resistive MHD model was employed in conjunction with flux injector boundary conditions to simulate HIT-SI operation. This computational model was employed to explore the effects of SIHI and Lundquist number (S) on sustained HIT-SI plasmas. Preliminary computational results showed very little plasma current formation at the Lundquist numbers comparable to that of the experiment ($\sim $5-10), a result that is in poor agreement with the experiment. To check these results, work has been undertaken to upgrade the existing computational model and to transfer it over to the newer version of NIMROD. Of particular interest are the improved resistive MHD and resistive MHD with the Hall term. The results of these simulations are to be compared with the experimental data. We will present our efforts and progress in this direction.   

Magnetic Diagnostics on HIT-SI Experiment

The HIT-SI equilibrium flux conserver is a CrCu shell with a 100ms L/R time. Pol. and tor. B-dot probes are embedded in the shell with a plasma facing s.s. disk to provide high bandwidth measurements. An extensive calibration of the probes from 10-200kHz has been carried out. Based on these calibrations, the probes can be digitized directly with much greater sensitivity at higher frequencies. The calibration and analysis procedures for reducing the measurements and an overview of the magnetic measurements will be presented.   

Development of rotating magnetic field coil system in the HIST spherical torus device

Coaxial Helicity Injection (CHI) is one of most attractive methods to achieve non-inductive current drive in spherical torus devices. The current drive mechanism of CHI relies on MHD relaxation process of rotating kink behavior [1], so that there is a possibility to control the CHI by using an externally applied rotating magnetic field (RMF). We have recently started to develop a RMF coil system in the HIST spherical torus device. Eight coils are located above and below the midplane at four toroidal locations so that the RMF is resonant with $n$ = 1 rotating kink mode driven by the CHI. In addition, the RMF coil set is installed inside a flux conserver of 5 mm thickness (cut-off frequency $\sim $ 170 Hz) so that the RMF penetrates into the plasma. The coil winding is made of 20 turns of enameled copper circular wires (1.5 mm$^{2}$ conductor cross section), covered with a thin stainless steal case of 0.5 mm thickness (cut-off frequency $\sim $ 710 kHz). The RMF system is driven by an IGBT inverter power supply (nominal current: 1 kA, nominal voltage: 1 kV) with an operating frequency band from 10 kHz to 30 kHz. The estimated amplitude of RMF neglecting effects of image current at the flux conserver is a few tens Gauss at around the magnetic axis. A preliminary experimental result will be shown in the conference. [1] M. Nagata, et al., Physics of Plasmas \textbf{10}, 2932 (2003).   

Ion flow measurements during the rotating kink behavior of the central column in the HIST device

Plasma flow is essentially driven in self-organization and magnetic reconnection process of compact spherical torus (ST) and spheromak in the helicity-driven systems. For example, when reversing the external toroidal field of ST, the direction not only of the plasma current but also of the toroidal ion flow is self-reversed during the formation of the flipped ST relaxed states. Mach probe measurement shows that the velocity of the ion flow reversed after the flip increases to about 20 km/s. We have been newly developing an ion Doppler spectrometer (IDS) system using a compact 16 or 64 channel photomultiplier tube (PMT) in order to measure the spatial profile of ion temperature and rotation velocity in the HIST device. The IDS system consists of a light collection system including optical fibers, 1 m-spectrometer and the PMT detector. The optical fibers covered with glass tubes are inserted into the plasma. The glass tubes can be rotated in the poloidal and the toroidal directions. The new IDS system will be applied to observations of ion temperature and plasma rotation in the flipped ST formation and in the MHD control of kinking behaviors of the central column by using the rotating magnetic field (RMF). Preliminary IDS results will be compared to those from Mach probe measurements in space.   

Interaction of Accelerated Compact Toroid with External Magnetic Fields

The potential use of accelerated compact toroids (SCT) to fuel magnetically confined fusion devices requires a clear understanding of the CT interaction with external magnetic fields. Previous experiment using simple probe diagnostics has illuminate the interaction physics [1]. With an array of new diagnostics, we will perform more detailed measurements of the interaction. With the new fast 2-D optical camera, the interaction in the target chamber can be systematically studied. The newly developed deflectometor can differentiate the effects on the main CT plasma versus the trailing plasma following the main CT. It is expected the external magnetic field will affect the magnetized CT differently than the un-magnetized trailing plasma. In addition the effect of the external magnetic field on the impurity ion in the CT will be studies using particle collection probes. In addition the oriental of the external field may tilt stabilize the CT after its detachment from the acceleration electrodes. *This work supported by U.S. DOE Grant DE-FG02-03ER54732. \newline [1] D.Q. Hwang, H.S. McLean, K.L. Baker, R.W. Evans, R.D. Horton, S.D. Terry, S. Howard, G.L. Schmidt, Nuclear Fusion, Vol. 40, No. 5, pg 897 (2000)   

Hall MHD Equilibrium of Accelerated Compact Toroids

We examine the structure and dynamics of the compact toroid's magnetic field. The compact toroid is dramatically accelerated by a large rail-gun Lorentz force density equal to $\mathbf{j \times B}$. We use magnetic data from the Compact Toroid Injection Experiment to answer the question of exactly where in the system $\mathbf{j \times B}$ has nonzero values, and to what extent we can apply the standard model of force-free equilibrium. In particular we present a method of analysis of the magnetic field probe signals that allows direct comparison to the predictions of the Woltjer-Taylor force-free model and Turner's generalization of magnetic relaxation in the presence of a non-zero Hall term and fluid vorticity.   

Plasma Density Gradient Profiles of Unconstrained CTs with an Array of Laser Deflectometers on CTIX

The Compact Toroid Injection Experiment (CTIX) is a plasma accelerator which can create compact toroid (CT) plasmas of controllable density and velocity. A CT is constrained by conducting walls during acceleration, but can be accelerated into a larger viewing chamber where the CT becomes unconstrained and is allowed to travel through free space. Since a laser deflectometer is a non-invasive line-integrated plasma density gradient diagnostic, an array of laser deflectometers at the viewing section of CTIX could profile density gradients of passing CTs in two dimensions with perturbing the plasma. A survey of density gradient profiles in two dimensions of unconstrained CTs traversing free space was conducted with an array of four temperature controlled laser deflectometers. These profiles of plasma density gradient were then used to estimate CT density profiles and CT total mass.   

Magnetic Field Effects on Accelerator-Region Gas Puffing on CTIX

By puffing axially-localized neutral gas into the accelerator region of CTIX prior to plasma formation and acceleration, high compact-toroid (CT) densities have been obtained. As gas puff density is increased, eventually spontaneous plasma breakdown occurs in the accelerator region, resulting in plasmas with high density, but with unsuitable internal field structure, timing, and location. Motivated by experiments which demonstrate the controlling effect of even weak magnetic fields on plasma breakdown in the formation region, azimuthally-symmetric magnetic fields will be applied in the vicinity of the accelerator valve in an attempt to increase the amount of gas which can be puffed without spontaneous breakdown. The effects of the localized magnetic fields of various configurations will be systematically examined, with the purpose of determining a regime of high density and high gas utilization efficiency during CT density buildup, thereby improving the usefulness of CT injection for fueling, target-compression, and other applications.   

Impurity Content of Compact Toroid Plasmas in CTIX

The Compact Toroid Injection Experiment (CTIX) produces a high density, high velocity hydrogen plasma which maintains its configuration in free space on a MHD resistive time scale. Repetitive injection of CT plasmas is being considered as a deep fueling technique for tokamaks such as ITER. In order to study the importance of impurities, several sets of silicon collector probes were exposed to the high velocity CT plasmas. Elemental analysis by Auger Electron Spectroscopy indicated the presence of oxygen, aluminum, iron, and copper in films up to 20 nm thickness (1000 CT interactions). Using a smaller number of CT interactions (10), implantation of the impurities was measured with depth profiling. The ordering of the range of the impurities (oxygen, aluminum, iron, copper) agreed roughly with TRIM calculations, however, the depth of the implants was less than that predicted for impurities moving with the CT velocity. Analysis of artificially introduced impurities and a discussion of the source of the intrinsic impurities will be discussed.   

Preliminary experiment of high-speed gas flow generation by a compact toroid injection into a gas neutralizer

A supersonic gas jet injection has been considered to be a new technique for future reactor fuelling and disruption mitigation in tokamak devices [1]. We have recently started to investigate a production of high-speed gas flow by using a compact toroid (CT) injection into a hydrogen gas neutralizer. The electron density of the CT plasma is 1$\sim $4 x10$^{21}$ m$^{-3}$, and the CT speed is 30$\sim $70 km/s in the preliminary experiment. The kinetic-energy measurements of ions and neutrals after the neutralization were carried out by using an electrostatic ion energy analyzer and time-of-flight technique. An enhancement of the H$_{\beta }$ emission level, a significant decay of the CT plasma density and the magnetic field profile have been observed after the neutralization when the neutral pressure is about 10$^{-3}$ Torr. It could be considered that high-energy neutral particles were generated by a charge exchange process from the CT plasma to the neutral particles. \newline [1] V. Rozhansky, et al., Nucl. Fusion \textbf{46}, 367 (2006).   

Spheromak merging studies in an oblate flux conserver in SSX

Work is underway on a new oblate flux conserver for spheromak merging studies on SSX. The oblate flux conserver has a $0.5~m$ inside diameter and $L = 0.28~m$ with a $6~mm$ copper wall. The outer electrodes mate to the flux conserver through a conical entrance region. The entire inner surface will be coated with tungsten. Initial studies will be performed with arrays of magnetic probes and ion Doppler spectroscopy (IDS). Fast magnetic probe arrays in quartz jackets with resolution of $1~mm$ will be installed for magnetic reconnection studies at the midplane. Low spatial resolution magnetic probes will map the equilibrium structure. The SSX IDS instrument measures with $1~\mu s$ or better time resolution the width and Doppler shift of either the nascent $C_{III}$ impurity $229.7~nm$ line or a doped $He_{II}$ impurity $468.6~nm$ line to determine the temperature and line-averaged flow velocity. Preliminary data will be compared with earlier merging results in a $0.4~m$ diameter, $L=0.6~m$ length prolate copper flux conserver in SSX. In prior merging studies we have measured $T_i \ge 50~eV$ and $T_e \ge 30~eV$ after all plasma facing surfaces are cleaned with helium glow discharge conditioning. Transient electron heating is measured with a 4-channel soft x-ray array and a $0.2~m$ vacuum ultraviolet spectrometer ($C_{III}~97.7~nm/C_{IV}~155~nm$ line ratio).   

Nonlinear driven resonance in magnetic self-organization and the feasibility of a spheromak reactor

A Taylor relaxed plasma (${\bf j}=k{\bf B}$ with $k$ a constant) under external magnetic helicity injection encounters resonances in spatial frequencies of its force-free eigenmodes. Such driven resonance underlies the physics of magnetic self-organization and determines the flux amplification in laboratory helicity injection applications. Here we show that for partially relaxed plasmas where the deviation from the fully relaxed Taylor state, for example, a flux-dependent $k$, is a function of the normalized flux $\chi/\chi_{a}$ with $\chi_{a}$ the poloidal flux at the magnetic axis, a modified driven resonance persists even if $k(\chi)$ has an order-unity variation across the flux surfaces. We will also explain why experimentally accessing such nonlinear resonance appears to hold the key for a potential spheromak reactor. Ref. X.Z.Tang, Phys. Rev. Lett. {\bf 98}, 175001 (2007).   

2D MHD simulations of the High to Ordinary Mode Transitions in MCX

The plasma in the Maryland Centrifugal Experiment (MCX) device makes an abrupt transition from a good confined state (H mode) to a poorly confined state (the O mode). To model this transition a 2D time-dependent MHD code is used to determine the dynamical equilibrium states of the MCX configuration. An additional momentum loss term is added to the system of equations to model the coupling of the plasma to the neutrals in the vicinity of the two insulators at the mirror throats. An input momentum source is treated as a control parameter to drive the poloidal rotation which in the machine is accomplished by the radial electric field and the ensuing ExB rotation. It is found that for small values of the source, the equilibrium state is not centrifugally confined enough and hence experiences additional drag from the neutrals in the vicinity of the insulators. However, at a critical forcing, the plasma makes an abrupt transition to a good centrifugally confined state in which the plasma has pulled away from the end insulator plates. As it pulls away the drags from the neutrals in the throat region decreases which further increases the rotation thereby leading to better centrifugal confinement. The good confined state is reached when the momentum source balances the diffusive damping.   

Magnetic Fluctuation Measurements in MCX

Initial results from magnetic probes on the Maryland Centrifugal eXperiment(MCX) provide details of the rotation and poloidal mode structure of magnetic fluctuations in the edge region. Eight magnetic coils placed azimuthally around the edge measure magnetic field changes in the axial direction during the plasma discharge. The auto and cross-correlation of the magnetic fields between the coils show that the magnetic fluctuations are dominantly convected by the ExB plasma rotation for several rotation periods before significant decorrelation. The rotation so inferred is in the $E\times B$ direction and its magnitude is consistent with earlier spectroscopic measurements on MCX. These findings help identify the dominant modes at the edge and indicate that there are a few low mode numbers that are dominant during the discharge. Also, the speed of rotation and fluctuation spectrum is found to change dramatically from the High Rotation (HR) state to a low rotation ordinary (O) state. In the near future, we plan to use probes which measure the magnetic field in all three directions near the edge of MCX. This will help us understand the magnetic structure and the basic instability in MCX.   

Spectral Results of the Magnetic Fluctuations Observed in MCX

The Maryland Centrifugal Experiment (MCX) is set up to study centrifugal confinement and supersonic rotation. MCX is a magnetic mirror machine with end fields up to 2T independent of the mid-plane magnetic field. A radial electric field created by biasing the inner electrode with respect to outer wall is used to drive azimuthal rotation, i.e., E x B rotation. Previously, a small number of Bdot coils have been employed at the edge of the plasma to investigate the modes of operation. Preliminary results show that there are dominant modes associated with the E x B rotation. In order to assess magnetic fluctuations and the E x B rotation fully, 25 Bdot coils mounted on various locations inside MCX are utilized. Here we present the analysis of the observed spectral modes by means of the power spectrum and the bispectrum to focus on the nonlinear coupling among various m-modes. We will also address low frequency magnetic field perturbations via proper filtering process.   

The Maryland Centrifugal Experiment(MCX)

We report new results on MCX : a) measurements of ion rotational velocity profiles show parabolic radial profiles that demonstrate shear in the plasma rotation exceeds the critical value for shear stabilization; b) measurements of the velocity profile also show the plasma may not be undergoing isorotation , a departure from ideal MHD; c) a new insulator has eliminated the transition from high-rotation (HR) mode to low rotation(O) mode; d) the scaling of maximum rotational velocity with applied voltage and B shows that rotational velocity is clearly limited from above by the Alfven velocity but determining if the critical ionization phenomena is operable is not conclusive. We also report on: a) plans to launch a plasma jet from a newly constructed gun to impart momentum directly to MCX and b) magnetic probe measurements of fluctuations at a variety of azimuthal, radial, and axial locations to evaluate MHD stability and its relation to velocity profiles. Plans for higher voltages and higher B fields will be discussed.   

Progress on H$_{\alpha}$ at MCX

The Maryland Centrifugal eXperiment uses a seven-chord H$_{\alpha}$ measurement system to measure absolute intensity levels of the Hydrogen Balmer-alpha line in a rotating plasma with mirror magnetic geometry. Recently, new mirror insulators were designed and implemented, resulting in suppressed O-mode operation. We present comparisons between H$_{\alpha}$ signals before and after the implementation of the new insulator. We also present progress in modeling neutral density for a rotating mirror geometry as well as relevant comparisons to experimental measurements on MCX. Lastly, we discuss upgrading the H$_{\alpha}$ measurement system to include a 16-chord mid-plane array.   

Experimental study on the velocity limits of magnetized rotating plasmas

An experimental study on the physical limits of the rotation velocity of magnetized plasmas is presented. A comprehensive campaign has been carried out on the MCX, a mirror magnetic field plasma rotating azimuthally, to ascertain what physical effects limit attempts to externally boost the velocity. The externally applied parameters that control the plasma characteristics -- applied voltage, external magnetic field and fill pressure -- are scanned across the entire available range of values. It is found that the plasma rotation velocity does not exceed the Alfven velocity, in complete agreement with the equilibrium requirements of magnetically confined plasmas. As the velocity approaches the average Alfven speed, further applied force does not result in an increase past this critical speed. Diamagnetic loop measurements show that the diamagnetically excluded flux increases as the square of the Alfven Mach number, as predicted by equilibrium MHD theory. Measured rotation velocities are also found to stay below the critical ionization velocity in hydrogen, a limit suggested by Alfven. However, an approach to a definite limit has not been proven yet largely because of voltage and magnetic field upper bounds dictated by the available experimental hardware.   

Study of magnetic dipole forbidden transitions in Large Helical Device and its application to impurity and $\alpha $ particle diagnostics in burning plasmas

Magnetic dipole forbidden (M1) transitions of Al (Z=13) to Xe (Z=54) emitted in visible and VUV ranges have been observed in Large Helical Device (LHD) and analyzed with level population calculation. It is found that the ratio of the M1 transition to usually used electric dipole (E1) transition gives clearly separated two ranges exhibiting density-independence and density dependence. Observation of orthogonal linearly polarized components of the M1 lines gives a completely different structure from the E1 transitions. Diagnostic applications to burning plasmas, i.e., impurity spectroscopy using the M1 transitions from high-Z elements such as Mo and W and alpha particle measurement using the ratio of the M1 to E1 transitions and the Zeeman-polarization technique are presented.   

Observation of Novel Instability by using Microwave Imaging Reflectometry in LHD

A novel instability with higher harmonics has been observed in the Large Helical Device (LHD) by using Microwave Imaging Reflectometry (MIR). The instability appears during NBI or ICRH heating, and it is radially localized near the rational surface with the rotational transform of unity. The density fluctuation has a fundamental frequency of 1 $\sim $ 10 kHz which depends on the ion temperature. The frequency is several times higher than the diamagnetic frequency of the thermal ions, and is much lower than the frequency of the Alfven Eigen modes. The similar spectrum is also observed in the magnetic probe signals. It is suggested that the mode may be destabilized by the energetic ions and related to the pressure gradient of the thermal ions.   

Magnetic Fluctuation Profile Measurement Using Optics of Motional Stark Effect Diagnostics in JT-60U

Motional Stark effect (MSE) diagnostics in JT-60U works as polarimeter to measure the pitch angle of magnetic field as well as beam-emission-spectroscopy (BES) monochromator simultaneously at 30 spatial channels. Fluctuation in the BES signal contains fluctuations in plasma density and pitch angle. In a high beta plasma with MHD activity, density fluctuation is measured at the same frequency as the n=1 magnetic fluctuation measured by pickup-coils outside the plasma. With correlation analysis of the BES signals, the density fluctuation profile is not only inverted near q=2 surface measured by the MSE, but also inverted at opposite toroidal angles at the same radial position. Thus, it is reasonably concluded that the fluctuation is induced by rotating magnetic islands spatially localized about q=2 surface. In the discharge, fluctuation at the beat frequency ( $f_{\mbox{PEM}} \pm f_{\mbox{n}} $ ) of pitch angle measurement ( $f_{\mbox{PEM}}$ ) and density fluctuation ( $f_{\mbox{n}}$ ) shows a signature of pitch angle fluctuation. The spatial structure of the pitch angle fluctuation is discussed.   

Fast ion collective Thomson scattering (CTS) diagnostic results at TEXTOR, ASDEX Upgrade and status of ITER design

In ITER, fast alpha particles born in fusion processes will account for up to 70{\%} of the heating power. Measurements of confined fast ions resolved in space, pitch angle, energy and time are needed to support improvements of current theories. Fast ion collective Thomson scattering (CTS) can meet this need. Here we present results from CTS on TEXTOR where a 150 KW 110GHz gyrotron scatters off fluctuations driven by NBI/ICRH fast ions. The 1D fast ion velocity distribution has been inferred, where the resolved direction and the measuring volume are defined by the scattering geometry. The spatial resolution is $\sim $10 cm while the temporal resolution is 4 ms. The build-up and slowdown of co-injected neutral beams are reported along with comparisons between co and counter beam ion dynamics. The measured decay and build-up of co NBI is in agreement with classical slowing down. First results from ASDEX Upgrade, where a 105 GHz system is installed are expected to be presented. Finally, the status of the 60 GHz CTS diagnostic design proposed for ITER is presented. Supported by U. S. DoE and EURATOM.   

The motional Stark effect with laser-induced fluorescence diagnostic

Traditional motional Stark effect (MSE) diagnostics exploit the polarization properties of light generated from a neutral hydrogenic beam via collisionally-induced fluorescence (CIF). MSE uses this information to determine a spatially resolved profile of the magnetic field pitch angle in a magnetized plasma. The use of laser-induced fluorescence with MSE on a dedicated diagnostic neutral beam enables an MSE pitch angle measurement at fields as low as 0.001 T, which cannot be achieved by CIF systems. The LIF system also affords the option of very precisely measuring the magnetic field magnitude as well as direction. The MSE-LIF diagnostic is under development in our laboratory, where we have a diagnostic neutral beam system, a dye laser, and a helicon plasma source. This poster will present the latest results relating to MSE-LIF measurements in plasma, as well as an analysis of the relative utility of magnetic field magnitude vs pitch angle measurements for equilibrium reconstruction.   

Velocity Field Analysis for Edge Turbulence Imaging

Techniques for extracting time-resolved 2-D velocity maps have been developed for turbulence imaging diagnostics. A hybrid technique combining optical flow and local pattern matching has been implemented to overcome the individual limitations of each when used with data of limited temporal and/or spatial resolution. The codes have been validated for a variety of test patterns of convective flow, including highly sheared cases. Recent work includes detailed consideration of the velocity divergence in the 2-D plane, and its significance to the derived results. We present comparison and validation studies to various artificial datasets with known velocity profiles, including sets with significant curl.   

Density fluctuation measurements with the microwave imaging reflectometry on TPE-RX

Electron density fluctuation in a large reversed-field pinch device TPE-RX has been investigated by using the microwave imaging reflectometry (MIR) system for the first time. This system illuminates the TPE-RX plasma with the 20 GHz microwave beam in O-mode and measures the reflection by a two dimensional detector array with spatial resolution of 4cm and temporal resolution of 1ms. Each detector signal has 3 components, such as the amplitude, the in-phase (I) and the quadrature (Q). The reflection surface motion is obtained from the rotation of the I-Q components of the MIR signals. Cross-spectral method is used for the analysis of the amplitude of the reflected wave. We investigate four different types of RFP plasma, such as the quasi-single-helicity (QSH) plasma, the pulsed poloidal current drive (PPCD) plasma, the sawtoothing high theta plasma and the NBI heated plasma. The fluctuations indicate that the plasma turbulence is dominated by the low frequency and long wavelength fluctuation components and the statistical dispersion relation shows the typical electron drift wave characteristics.   

Two-dimensional Thomson Scattering Measurement Using Multiple Reflection and the Time-of-Flight of Laser Light on TS-4

A two-dimensional Thomson scattering (2-D TS) measurement system is being constructed on TS-4 device with major/minor radii of 0.5m/0.3m and its main tasks of plasma merging and confinement of ST (Spherical Tokamak) plasma. This system is intended to measure $T_{e}$ in the range of 20-200eV for $n_{e}\sim 10^ {20}$m$^{3}$ with a spatial resolution of 160mm (four points) in the $r$-direction and 130 mm (three points) in the $z$- direction. The new ideas of our 2-D TS system are (1) to reflect YAG laser light multiple times by mirrors to cover the whole $r$-$z$ plane of the ST plasma, and (2) to utilize the time delay of the scattered light along the laser beam in order to reduce the necessary number of spectrometers and detectors. In a preliminary experiment, Rayleigh scattering light from two measurement points and Raman scattering light from three measurement points were successfully measured by a single spectrometer as their time evolutions, suggesting that the basic principle of the 2-D TS system functions effectively. To prepare for the TS measurement, the gas pressure dependency of Rayleigh and Raman scattering lights were observed for absolute calibration of the system. The first result of our TS system will be presented.   

Electron Density Profile Measurements of a Field-Reversed Configuration Using an Optical Interferometer

A laser interferometer system operating at 633 nm is being used to measure the electron density of field-reversed configurations (FRCs) produced by the magnetized target fusion (MTF) experiment at the Air Force Research Laboratory (AFRL). The design is a scaled-down version of an eight-chord system previously used to provide time-resolved information about the spatial distribution of electron density in a similar FRC experiment [E.~L.~Ruden {\sl et al.}, {\it Rev.~Sci.~Instrum.}~ {\bf 77}, 103502 (2006)]. Here, a fanned array of laser beams probes the plasma through the FRC midplane along four different chords. In addition, our design features the option of diverting any or all of the four probe beams into single-mode optical fibers whose collimated outputs can be used to probe different axial locations simultaneously [L.~M.~Smith {\sl et al.}, {\it Rev.~Sci.~Instrum.}~{\bf 74}, 3324 (2003)]. This arrangement enables us to place the interferometer system's optical table at a safe distance from the MTF-FRC experiment when destructive tests involving plasma compression by a solid metal liner imploded by the Shiva Star capacitor bank are attempted. Data from the four-chord system and the system with the fiber-optic probe beam modification will be presented.   

Three dimensional full-wave simulations of reflectometry in toroidal plasma

A three-dimensional wave propagation code, developed specifically to simulate correlation reflectometry in large scale fusion plasmas is described. The code extends an algorithm previously implemented in 2D [E. J. Valeo, G. J. Kramer, and R. Nazikian, Plasma Phys. Control. Fusison {\bf 44} (2002) L1-L10], in which separate computational methods in the vacuum, underdense and reflection regions of the plasma are implemented in order to obtain the high computational efficiency necessary for correlation analysis. Simulations of ITER plasma are presented which demonstrate the efficiency of the method.   

A Multi-Channel, Frequency Comb Doppler Reflectometry System

Enhanced diagnostic capabilities are needed for the study of turbulent transport, zonal flows, and global modes (TAE, NTM, etc.) in fusion plasmas. Doppler reflectometry is a microwave diagnostic technique that produces localized measurements of intermediate-scale ($k_\bot \rho _i \sim 1)$ density fluctuations and turbulence flow. A microwave beam is launched at an angle with respect to normal to the cutoff layer; backscattering occurs for density fluctuations near the cutoff layer according to the Bragg condition. The incident angle can be varied to probe the $k$-spectrum of the turbulence and the Doppler shift of the return signal provides the poloidal velocity of the fluctuations. A comb generator will be used to create 8 distinct launch frequencies, separated by $\sim $2 GHz, in the 34-50 GHz range. The receiver will consist of a local oscillator at 32 GHz and a high-frequency mixer. The down-converted output, ranging 2-18 GHz, will be amplified, power split, and frequency selected via filter bank. Amplitude and phase information will be obtained by using radio frequency quadrature mixers. Technical details and results from laboratory testing will be presented.   

ECE Imaging Bandwidth Upgrade for TEXTOR

The 128 channel 2-D Electron Cyclotron Emission (ECE) Imaging system collects time-resolved 16$\times $8 images of electron temperature profiles and fluctuations on the TEXTOR tokamak. This instrument was upgraded in February 2007 with new wideband ECE electronics which increased the instantaneous frequency coverage by $>$50{\%} to 6.4 GHz with a corresponding increase in horizontal plasma coverage. Frequency extenders have been developed to combine modules together to double the instantaneous coverage to 12.8 GHz. Technical details regarding both the electronics upgrade and the frequency extenders as well as the preliminary physics results will be presented. Implementation of a similar but new ECEI instrument on the DIII-D tokamak will be extensively discussed.   

Development of free-standing diffractive optical elements as light extractors for burning plasma experiments

Optical diagnostics will be critical for the operation and performance assessment of burning plasma experiments, such as ITER. At the same time, extracting light for these diagnostics with reflective mirrors becomes difficult in the burning plasma environment, due to prolonged exposure to plasma and nuclear radiation. As an alternative, we explore free-standing diffractive optical elements, such as transmission gratings and zone plates. Since in the case of diffractive extractors the light is deflected by periodic slits rather than a surface, they may withstand plasma exposure with less degradation of their optical properties. To investigate this possibility we developed free-standing transmission gratings for the visible range and exposed them in to conditions resembling or exceeding those expected for the ITER `first mirrors'. The results of this study indicate that the gratings can withstand high heat fluxes and plasma and energetic radiation bombardment. In addition, in contrast to the reflective elements, the extraction capabilities of the diffractive elements can also improve with plasma exposure, due for instance to shaping and thinning of the grating bars by plasma erosion. Work supported by US DoE grant DE-FG02-99ER54523.   

Implementation of Language Interoperability Interfaces for NTCC transport models as part of FMCFM project

A new generalized interface to the transport modules and libraries from the National Transport Code Collaboration (NTCC) module library~[1] is presented. The interface is created as a part of the Framework for Modernization and Componentization of Fusion Modules (FMCFM) project. The interface utilizes the technologies of encapsulation and polymorphism available in Fortran-95 that replace the COMMON BLOCK approach typical for Fortran legacy codes and allows us to create a generalized interface to the reduced transport modules. The new interface facilitates access to the transport models from integrated modeling codes and allows interlanguage interfaces using a new library of C++/Fortran-95 wrappers. This library also includes a collection of subroutines for data access from C/C++ to the Fortran 90 derived data structures. The new interface to transport modules has been applied to the the GLF23 and MMM95 transport models. The functionality is demonstrated in Framework Application for Core-Edge Transport Simulations (FACETS) project. \newline \newline [1] A. H. Kritz \textit{et al.} Comp. Phys. Communications \textbf{164} (2004) 108.   

Parallel, Implicit, Finite Element Solver

A parallel, implicit, finite element solver is described for solutions to the ideal MHD equations and the Pseudo-1D Euler equations. The solver uses the conservative flux source form of the equations. This helps simplify the discretization of the finite element method by keeping the specification of the physics separate. An implicit time advance is used to allow sufficiently large time steps. The Portable Extensible Toolkit for Scientific Computation (PETSc) is implemented for parallel matrix solvers and parallel data structures. Results for several test cases are described as well as accuracy of the method.   

New quasi-Newton solver for transport equations

A new quasi-Newton algorithm has been developed for systems in which the Jacobian has a block structure, as is the case for finite-difference approximations of transport equations where the fluxes depend only on the local field values and their gradients. A primary goal of this work is to minimize the number of numerically expensive flux calculations (e.g. diffusivities). Secondary design considerations were $2^{nd}$ order temporal and spatial discretization error, good numerical stability, and a modular design. Like the most common quasi-Newton algorithm, the Broyden method, our new quasi-Newton approach, the Block Hyper-Secant (BHS) approximation, uses flux evaluations from previous Newton iterations to approximate the Jacobian. If the flux evaluations dominate the computation time, the approximate Jacobian is thus free. Unlike Broyden, the BHS approximation converges toward the finite-difference Jacobian after sufficiently many iterations. An implicit transport solver, $2^{nd}$ order in time and space, has been implemented using the BHS solver to calculate the field increments. Numerical studies will be presented of its spatial and temporal accuracy as well as stability for time steps exceeding the CFL limit by many orders of magnitude. The FACETS FSP project has started using the BHS solver for core transport simulations and preliminary results will be presented.   

Mathematical Properties of the Flowing MHD Equilibrium Equations

Experiments have observed significant toroidal and poloidal flows in their plasmas [1-3]. This has led to the need for a flowing equilibrium solver that is equipped to handle both fixed and free boundaries. In order to achieve this, the mathematical properties of the flow equilibrium equations need to be better understood. Difficulty arises when analyzing these equations since they are not only fully non-linear, but also the differential operator itself is coupled to an algebraic equation. We discuss the method and process used to formulate the equilibrium problem with flow effects in a computationally tractable form and the methods available to solve the resulting equations. Initial results from an implementation of the equilibrium equations are also presented. \newline \newline [1] S.K. Erents, A.V. Chankin, G.F. Matthews, P.C. Stangeby, Plasma Phys. Controlled Fusion 42, 905 (2000). \newline [2] T.S. Taylor, H.St. John, A.D. Turnbull, et al. Plasma Phys. Controlled Fusion 36 B229 (1994). \newline [3] M. Ono, S.M. Kaye, Y.K.M. Peng et al. Nucl. Fusion 40, 557 (2000).   

Mesoscopic Detailed Balance Representations of Nonlinear Physics

We emphasize the similarity between entropic Lattice Boltzmann (ELB) and quantum lattice gas representations of nonlinear physics. At each space-time grid point, the excited state of a qubit encodes the probability that a mesoparticle moves along a lattice link. All the particle-particle interactions can be mapped onto a local unitary collision operator which locally entangles all the quibts at that node. This quantum entanglement is then spread throughout the lattice by unitary streaming. In the classical limit, there exists a fundamental discrete entropy function, and the collision operator is restricted that the post-collision distributions lie on a constant entropy surface and leads to a detailed balance ELB algorithm. This has been exploited in the solution of Navier-Stokes and MHD turbulence with div B = 0. On the other hand, with just 2 qubits/lattice site one can recovery the 3D Nonlinear Schrodinger equation of nonlinear optics and the Gross-Pitaevskii equation of BEC states under an appropriate unitary sequence of collide-stream. In particular, we examine solitary wave solutions of the GP equation and vortex nucleation.   

A new nonlinear collision method for a particle code

A new nonlinear collision operation method for a particle code is presented, which does not use the Monte Carlo scheme. Particle information is gathered on a 2D velocity grid and the particle distribution function is obtained by a penalized spline operation which conserves mass, momentum, energy, and entropy. After performing the fully nonlinear Rosenbluth-McDonand-Judd Fokker-Planck operation using advanced mathematical methods, the collision information is sent back to the particles. The new collision operation can reduce the discrete particle noise while performing physical Coulomb collisions. It can also significantly reduce the required frequency of collision operations due to absence of the Monte Carlo noise. Comparison with a well-known binary collision method will be given. The conservation properties will be discussed.   

A step towards addressing the temporal multi-scale problem.

Plasmas display multi-scale features in space and in time. While application of methods such as Adaptive Mesh Refinement have made progress with regards to resolving multi-scale features in space, the temporal multi-scale nature of a two species plasma remains a challenging problem. Spectral Differed Correction (SDC) is intended to address the temporal multi-scale problem. In this work we consider the application of SDC to a particle formulation of the Vlasov-Poisson system as a way of accelerating temporal convergence. In particular, we consider the two-stream instability, as particle trapping is known to be an issue for temporal acceleration methods.   

Boundary Integral Corrected Particle In Cell

Numerical heating is a serous problem in PIC modeling of cross field Diffusion. Recent work by the author has shown that for, electrostatic problems, the Boundary Integral Treecode (BIT) has far less numerical heating than traditional PIC and that numerical heating can be nearly eliminated if regularization is added to the BIT field solver. In this work we consider the application of BIT as a sub-cell method within each PIC cell, where the boundary conditions on BIT come from the fields computed on the PIC mesh. The goal is to minimize numerical heating in PIC while allowing for mesh spacing in PIC to be much greater than a Debye length. Our overall objective is to inherit the parallel capability of legacy PIC codes while providing high accuracy.   

PARSEK: a Parallel Software Package for Implicit Particle-in-Cell Simulations

A C++ software package, called PARSEK, for Particle-in-Cell(PIC) plasma simulations on parallel computers is presented. PARSEK computational engine is based on the fully implicit solution of discretized three dimensional Maxwell's equations and particle equation of motion. The implicit method allows to describe effectively low-frequency plasma phenomena without paying the severe restrictions of explicit numerical schemes on simulation time steps and grid spacing. The fully implicit PIC method is now developed on parallel computer architecture. With implicit numerical schemes and parallel software architecture, PARSEK extends considerably time and space scale domains of PIC simulations. PARSEK software components, with emphasis on the development of the implicit PIC method on parallel computers, and a suite of applications, such as magnetic reconnection and relativistic streaming instabilities, are described.   

The EMPOWER Code: Electro-Magnetic Particle Operation With Enhanced Resolution

Large-scale full PIC simulations play a crucial role in the modeling of laser-plasma interactions, accelerators, HPM devices and magnetic reconnection. These simulations ubiquitously employ uniform meshes, which severely limits their CPU speed and in many cases makes high-resolution runs prohibitive even on massively parallel computers. On the other hand, inadequate spatial resolution of realistic features (localized plasma volumes, device boundaries, etc.) is known to result in unacceptable errors. Structured adaptive mesh refinement (SAMR) has successfully been applied to fluid dynamics and MHD simulations. However, extending SAMR to practical electromagnetic particle-in-cell (PIC) models has proven to be nontrivial due to a number of additional numerical challenges, with spurious wave reflection and macro-particle self-force at the coarse-fine mesh interfaces being the most severe. These approximation errors typically result in a significant loss of simulation accuracy, energy/momentum non-conservation and long-time instabilities. We review our progress in resolving these issues in our new EM-PIC code, EMPOWER. We demonstrate the efficiency and accuracy of the new techniques on realistic examples related to simulations of high-power EM pulses and energetic particle beams.   

A New Simulation Algorithm Combining Fluid and Kinetic Properties

Complex Particle Kinetics (CPK) [1,2] uses particles with internal degrees of freedom in an effort to simulate the transition between continuum and kinetic dynamics. Recent work [3] has provided a new path towards extending the adaptive particle capabilities of CPK. The resulting algorithm bridges the gap between fluid and kinetic regimes. The method uses an ensemble of macro-particles with a Gaussian spatial profile and a Mawellian velocity distribution to represent particle distributions in phase space. In addition to the standard PIC quantities of location, drift velocity, mass, and charge, the macro-particles also carry width, thermal velocity, and an internal velocity. The particle shape, internal velocity, and drift velocity respond to internal and eternal forces. The particles can contract, expand, rotate, and pass through one another. The algorithm allows arbitrary collisionality and functions effectively in the collision-dominated limit. We will present details of the algorithm as well as the results from several simulations. [1] D. W. Hewett, \textit{J. Comp. Phys}. \textbf{189} (2003). [2] D. J. Larson, \textit{J. Comp. Phys}. \textbf{188} (2003). [3] C. Gauger, \textit{et.al.,} \textit{SIAM} \textit{J. Numer. Anal. }\textbf{37} (2000).   

Discrete-Event Simulation of Poisson-Based Particle Systems

We describe a new algorithm for simulating multi-scale kinetic (N-body) systems, where particles interact via potential forces obtained from the solution of Poisson's equation. Such models range from electrostatic plasma to fluid to astrophysical (gravitational) applications. Our technique is based on two novel principles: (i) we use a self-adaptive, \textit{discrete-event simulation} (DES) technique [1,2] for the asynchronous integration of particle equations of motion; (ii) we find the particle forces by convolving mesh-averaged Green's functions with asynchronous \textit{changes} to the particle (charge or mass) density, computed with respect to periodically updated reference states of the system. We demonstrate the new approach by providing examples of space-charge beam simulations. [1] H. Karimabadi, J. Driscoll, Y.A. Omelchenko, N. Omidi, J. Comp. Phys. 205, 755 (2005). [2] Y.A. Omelchenko, H. Karimabadi, J. Comp. Phys. 216, 153 (2006).   

A robust, efficient equidistribution 2D grid generation method

We present a new cell-area equidistribution method for two- dimensional grid adaptation [1]. The method is able to satisfy the equidistribution constraint to arbitrary precision while optimizing desired grid properties (such as isotropy and smoothness). The method is based on the minimization of the grid smoothness integral, constrained to producing a given positive-definite cell volume distribution. The procedure gives rise to a single, non-linear scalar equation with no free-parameters. We solve this equation numerically with the Newton-Krylov technique. The ellipticity property of the linearized scalar equation allows multigrid preconditioning techniques to be effectively used. We demonstrate a solution exists and is unique. Therefore, once the solution is found, the adapted grid cannot be folded due to the positivity of the constraint on the cell volumes. We present several challenging tests to show that our new method produces optimal grids in which the constraint is satisfied numerically to arbitrary precision. We also compare the new method to the deformation method [2] and show that our new method produces better quality grids. [1] G.L. Delzanno, L. Chac\'{o}n, J.M. Finn, Y. Chung, G. Lapenta, \textit{A new, robust equidistribution method for two-dimensional grid generation}, in preparation. [2] G. Liao and D. Anderson, A new approach to grid generation, Appl. Anal. 44, 285--297 (1992).   

A Mesh-Free Method for the Simulation of Magnetic Diffusion

Magnetohydrodynamics (MHD) plays an important role in various physical systems at large and small scales. Recently, mesh-free methods such as Smoothed Particle Magnetohydrodynamics [1] (SPMHD) have been developed to study these systems by simulating magnetic fields in the presence of conducting media. However, these methods currently do not incorporate realistic models for electrical resistivity, which can significantly affect the dynamics of the system by introducing magnetic diffusion, thereby altering the field's topology. We describe a Meshless Local Petrov Galerkin (MLPG) method that solves such magnetic diffusion problems using local weak forms composed of mesh-free shape functions. This MLPG method accommodates inhomogeneous and anisotropic electrical resistivity models and allows the magnetic field to be evolved implicitly in time. We have assembled several test problems of interest in order to verify the method. Ultimately, we aim to combine this MLPG method with a form of SPMHD in order to treat realistic resistive magnetohydrodynamic systems. This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. \newline [1] D. J. Price, J. J. Monaghan, Mon. Not. Roy. Astr. Soc. Volume 348 Issue 1 pp. 123-138 (2004)   

Solution of the Boltzmann kinetic equation for arbitrary collisionality

Solving the nonlinear Boltzmann kinetic equation by traditional explicit numerical methods becomes increasingly difficult and costly as collisionality increases. However, many problems of scientific interest span the range from nearly collisionless to highly collisional regimes and remain beyond the reach of such methods. Thus, we develop an implicit solution technique to efficiently solve the Boltzmann equation for arbitrary collisionality. The technique builds upon methods developed for radiation transport and can be applied to a variety of numerical discretizations. As an example, we apply the method to a one-dimensional characteristic solution of the integral Boltzmann kinetic equation with Krook collision operator and a rigid elastic spherical atomic interaction potential. The technique can be extended to higher dimensions, applied to multiple atomic species, and is valid for more general interaction potentials. We present results for steady-state problems of Fourier flow and Couette flow over a large range of Knudsen numbers, and compare these with analytic results obtained using Chapman-Enskog theory.   

Regions of Validity for Common Plasma Models

Common plasma models, consisting of the kinetic, two-fluid ten-moment, two-fluid five-moment, and MHD descriptions, are reviewed. The assumptions used in the derivation of the fluid models are discussed, in particular the limits of their validity. Specific assumptions about the collisionality with regard to the thermalization times are explored. Requirements for model closure will be examined, paying attention to the restrictions on the distribution function. How these assumptions are different between the two-fluid ten-moment, two-fluid five-moment and MHD models will also be examined. Dispersion relations for the resulting fluid descriptions will be derived, and the associated physics captured will be compared.   

Stability of the Long Wavelength Limit of ETG Modes

The stability of long wavelength electron temperature modes is investigated (k$_\theta \rho_e \sim$ O(.1). The effects of kinetic ions as well as trapped electrons are included and discussed.   

Nonlinear finite-Larmor-radius effects in reduced fluid models

The polarization and magnetization effects associated with the process of dynamical reduction leading to nonlinear gyrokinetic theory [1] are shown to introduce nonlinear finite-Larmor-radius (NFLR) effects into nonlinear reduced-fluid equations [2]. These intrinsically nonlinear FLR effects, which are associated with the transformation from guiding-center phase-space dynamics to gyrocenter phase-space dynamics, are different from standard FLR corrections, which are associated with the transformation from particle phase-space dynamics to guiding-center phase-space dynamics. The reduced fluid equations with NFLR corrections are derived from a variational principle and, thus, automatically possess an exact energy conservation law. Simulation results show agreement with linear theory, nonlinear energy conservation, and mode coupling of Alfven and sound waves. \newline [1] A.J. Brizard and T.S. Hahm, Rev. Mod. Phys. {\bf 79}, 421 (2007). \newline [2] A.J. Brizard, Phys. Plasmas {\bf 12}, 092302 (2005).   

Electrostatic turbulence on transport time scales

Simulating electrostatic turbulence on transport time scales requires retaining a complete turbulence modified neoclassical (and classical) transport description, including all the axisymmetric radial neoclassical and zonal flow electric field effects, as well as the turbulent transport normally associated with drift instabilities. Neoclassical electric field effects are particularly difficult to retain since they require evaluating the ion distribution function to higher order in gyroradius over background scale length than standard gyrokinetic treatments. To avoid extending gyrokinetics an alternate hybrid gyrokinetic-fluid treatment is formulated that employs higher order moments of the full Fokker-Planck equation to remove the need for a higher order gyrokinetic distribution function. The resulting hybrid description is able to model all electrostatic turbulence effects with wavelengths much longer than an electron Larmor radius such as the ion temperature gradient (ITG) and trapped electron modes (TEM).   

Development of a Grid-Based Gyrokinetic Simulation Code

A new grid-based code is being developed for solving the gyrokinetic equation in tokamak geometry. This development builds on the experience gained with the CYGNE project [M. Brunetti \textit{et. al}, Comp. Phys. Comm. \textbf{163}, 1 (2004)], which solved the electrostatic drift-kinetic equations in a cylindrical system using a semi-Lagrangian approach. This new code makes use of efficient and flexible software modules optimized for parallel platforms. Preliminary results in reduced geometry, in particular slab and cylindrical, will be presented.   

A Low Moment Kinetic MHD Simulation Model

A wide variety of low-frequency macroscopic plasma phenomena are well described assuming quasi-neutrality, neglecting the displacement current and obtaining the electric field with a generalized Ohm's law. With this in mind, one can formulate the kinetic problem using ion density and ion flow moments. Kinetic electron physics enters via the electron pressure term in the generalized Ohm's law. Here, we formulate and test such a model with kinetic ions and an equation of state for the electrons. Whistler waves, shear Alfven waves (with finite gyro-radius corrections) and ion acoustic waves are present in the homogeneous plasma problem. Simulation results with this model are compared to the linear dispersion relation, including ion Landau damping. This simple kinetic particle model based on evaluating lower moments identically models the physics of more sophisticated extended-MHD models where ion kinetics closes via higher moments.   

Discrete particle noise in gyrokinetic PIC simulations of plasma turbulence

The studies of discrete particle noise have been done based on the gyrokinetic simulations of plasma turbulence using the gyrokinetic toroidal particle code (GTC). Statistical properties and associated transport of random fluctuations are first studied in a system with subcritical background gradients, such that no instabilities develop. Simulations in the parameter regime approaching marginality from below have subsequently been done, to study the effects of nonlinearity of the dielectric constant. The fluctuation spectra have been constructed from the direct simulation measurements of electrostatic potential. The noise- driven transport has been calculated using the quasilinear expression for the diffusivity. The obtained theoretical value for the diffusion coefficient is compared with the corresponding value obtained from the simulation, demonstrating good agreement. It has been shown that for the realistic parameters, the noise driven transport depends linearly on the entropy of the system, which, in particular, makes possible to estimate the noise contribution to the heat conductivity during simulations.   

Collisionless Heating in Gyrokinetic Turbulence

Heating in weakly collisional, turbulent plasma in the gyrokinetic regime (strong guide field, low frequencies compared to cyclotron frequencies, small perturbations, weak or strong turbulence) is usually associated with Landau and Barnes damping, which in turn are associated with parallel acceleration of particles by turbulent electric and magnetic fields. We discuss a novel form of heating observed in gyrokinetics which is distinct from these conventional processes. A simple theoretical framework is presented to explain the mechanism, which might be called ``perpendicular phase mixing.'' The theoretical framework allows one to distinguish and separate two components of heating (acceleration and thermalization) and to identify different mechanisms for each. Numerical results are shown which support the theory.   

Minimal models of finite Larmor radius effects on non-diffusive transport in two-dimensional plasmas

In order to gain understanding of non-diffusive transport in a simplified regime, we investigate minimal but non-integrable models for chaotic advection based on the Hasegawa-Mima limit of the gyrokinetic equation\footnote{del Castillo Negrete, Phys. Fluids 10, 1998}. These prescribed streamfunction models exhibit Lagrangian turbulence for passive tracer particles in the flow. In particular, particles execute L\'evy flights as they drift between vortices and surrounding zonal flows. We give the ensemble of tracers a Maxwellian distribution of gyroradii, which allows us to report on finite Larmor radius (FLR) effects. Measurements of transport for an ensemble of such trajectories shows non-diffusive scaling of the variance, $\sigma^2$, such that $\sigma^2 \sim t^{\alpha}$, where $1<\alpha<2$. We show that the shape and the spatio-temporal scaling of the Lagrangian propagator can be modeled with fractional diffusion equations currently used to study non-local transport in plasmas.~\footnote{del Castillo Negrete, Phys. Plasmas, 13 082308, 2006}. We find, as expected, that a larger average Larmor radius causes more particles to free-stream instead of travel in the stochastic layer. We also report on measures of the velocity correlations for passive particles in the flow, as this may be a useful technique for probing gyrokinetic turbulence.   

The role of conserved quantities in turbulence simulations

Direct numerical simulations of plasma turbulence have become an important tool for interpreting experimental data from tokamaks. There is, however, relatively little exploration of the fluctuation data that is produced by gyrokinetic simulations in the literature. In preparation for more detailed experimental validation of predictions from gyrokinetic simulations of plasma turbulence, we present studies of decaying turbulence and the influence of the conserved quantities to the cascading processes. Therefore we study first two simplified models: the Hasegawa-Mima model and a second model that allows for finite ion temperatures in the Hasegawa-Mima framework. Both models are studied using a spectral fluid code and a PIC code. The main focus is on how increasing the ratio of ion to electron temperature changes the cascading behavior. We will also discuss how the different simulation algorithms treat fine-scale velocity-space structure.   

Global gyrokinetic simulations using coupled flux-tubes

A full treatment of the transport problem in modern fusion devices requires simultaneous resolution of rapidly-evolving, small-scale turbulence and slowly-evolving, large-scale variation of background profiles. The multiscale nature of the problem makes it computationally expensive. Consequently, relatively few high resolution global simulations exist. We extend the continuum gyrokinetic code GS2 to explore the use of coupled flux-tube simulations to simulate global plasma dynamics efficiently. Coupling between flux-tubes is achieved by solving the recently developed gyrokinetic transport equations of Wang, Plunk and Cowley. This allows us to obtain the self-consistent, steady-state, background profiles and corresponding turbulent fluxes. We present and discuss preliminary results.   

Plasma Turbulence Simulation and Visualization on Graphics Processors: Efficient Parallel Computing on the Desktop

Direct numerical simulation (DNS) of turbulence is computationally very intensive and typically relies on some form of parallel processing. Spectral kernels used for spatial discretization are a common computational bottleneck on distributed memory architectures. One way to increase the efficiency of DNS algorithms is to parallelize spectral kernels using tightly-coupled SPMD multiprocessor hardware architecture with minimal inter-processor communication latency. In this poster we present techniques to take advantage of the recent programmable interfaces for modern Graphics Processing Units (GPUs) to carefully map DNS computations to GPU architectures that are characterized by a very high memory bandwidth and hundreds of SPMD processors. We compare and contrast the performance of our parallel algorithm on a modern GPU versus a CPU implementation of several turbulence simulation codes. We also demonstrate a prototype of a scalable computational steering framework based on turbulence simulation and visualization coupling on the GPU.   

Electrostatic kinetic turbulent cascade of entropy in magnetized plasmas

Upon the outstanding agreement of Goldreich \& Sridhar theory on astrophysical MHD turbulence with the assumption of anisotropy and critical balance [1], one may construct a gyrokinetic turbulent theory to explore the microscale behavior below the ion gyroscale [2]. In the global regime, it is shown that the fluctuations corresponding to Alfv\'en dynamics cascade independently from other fluctuations and that they don't exchange energy with one another as far as reduced MHD ordering holds. Applying the similar ordering to kinetic regime, we are led to gyrokinetic equations, which again support the cascades of kinetic Alfv\'en and compressive fluctuations without energy exchange. Thus we may conjecture that each fluctuation component exchanges energy at the ion gyroscale due to the strong coupling and start to cascade without energy exchange again below. Performing electrostatic decaying turbulence simulations with Boltzmann electrons using the gyrokinetic code {\tt AstroGK}, we here show the first computational results of the one component, entropy cascade in the absence of kinetic Alfv\'en fluctuations, below the ion gyroscale. The preliminary calculation shows that the turbulent spectra agree very well with the predicted theory. [1] P.~Goldreich \& S.~Sridhar, Astrophys. J. {\bf 438}, 763 (1995). [2] A.~A.~Schekochihin {\it et al}., submitted to Astrophys. J.   

Excitation of geodesic acoustic modes by drift waves and ion temperature gradient modes

We will present mode-coupling analysis for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves as well as toroidal ion temperature gradient (ITG) modes. Both this studies indicate that a coherent three-wave interaction is the primary process by which GAMs can be excited. Furthermore the frequency matching condition provides a prediction of the characteristic radial scale-length of GAMs which is in reasonable agreement with observations and simulations. The study also indicates why GAMs are preferentially excited in the edge region of toroidal magnetic confinement devices.   

Transport and the neoclassical tearing mode: Slab geometry

Due to very long discharges in ITER, NTMs can potentially grow to large widths, increasing transport and significantly degrading confinement. Understanding the processes of the island growth and their impact on the transport is thus of crucial importance. We are presenting a model of the NTM based on an expansion of the Fokker-Planck equation. As a first step, we will consider the islands in a curvature-free slab geometry (see also [1]). We are interested in the islands of the size such that the parallel transport around the island along the magnetic field lines happens on the same time scale as the radial transport across the island, $\chi_\|/l_\|^2 \sim\chi_\perp/w^2$. Assuming classical diffusion along the field lines and gyro-Bohm-like transport in the perpendicular direction, we obtain the scaling for the island width as $w \sim\sqrt{\rho_i L}$, which is the minimum island width for bootstrap drive (due to profile flattening). Using $\rho^{*1/2}$ as the expansion parameter, solution of the Fokker-Planck equation yields 2-D equations for the evolution of the electron and ion distribution functions. These equations are solved subject to boundary conditions provided by matching to an external MHD solution. \newline \newline [1] S.J. Allfrey, P. Popovich and S.C. Cowley, `The Neoclassical tearing mode: An anomalous transport process' (this conference).   

Hybrid Simulation of Ion Acoustic Waves Including Coulomb Collisions

Kinetic simulation of collective phenomena including Coulomb collisions in inhomogeneous plasma presents significant multi-scale challenges. When the ratio of the collisional-mean-free-path of an ion or electron species to the local scale length of the plasma properties or the electromagnetic fields varies from very much greater than unity (kinetic limit) to very much smaller than unity (fluid limit) over a domain of interest, comprehensive simulation becomes difficult; and a brute-force, first-principles approach is typically impractical because of the severe computational stiffness of the underlying physics. This paper reports progress on the development of a kinetic-fluid hybrid technique for plasma simulation intended to address such multiple scale situations. A specific application to the simulation of ion acoustic waves including both Landau damping and Fokker-Planck Coulomb collisions is presented.   

A Hybrid Monte Carlo Method for Coulomb Collisions

This presentation describes a hybrid computational method for Coulomb collisions in a plasma that combines a Monte Carlo particle simulation and a fluid dynamic solver in a single uniform method throughout phase space. The new method is based on a hybrid representation of the velocity distribution function $f(v)$, as a combination of a Maxwellian equilibrium $M(v)$ and a collection of discrete particles $g(v)$. The Maxwellian $M$ evolves in space and time through fluid-like equations, and the particles in $g$ convect and collide through Nanbu's Monte Carlo particle method (PRE 1997). Interactions between $M$ and $g$ are represented by a thermalization process that removes particles from g and includes them in $M$ and a dethermalization process that samples particles from $M$ and inserts them into $g$. As test cases for the hybrid method, we have used relaxation of an anisotropic Maxwellian and evolution of a bump-on-tail.   

Simulation of sheath problems with an accelerated Monte Carlo method

We simulate the interactions between a plasma and an absorbing wall in a confined volume with an accelerated Monte Carlo method for Coulomb Collisions. We treat ions as particles and the electrons to be continuum. Our method is based on the earlier work developed in the context of rarefied gas dynamics by Pareschi and Caflisch (J. Comp. Phys, 1999) and the Coulomb collision model developed by Nanbu (PRE 1997). The hybrid formulation combines particle and continuum methods and uses a thermalization and dethermalization procedure to accelerate the computation while retaining accuracy of the solution. We investigate sheath formation and compare the simulation results between Nanbu's particle method and the hybrid method.   

The neoclassical tearing mode: An anomalous transport process

The Neoclassical tearing mode (NTM) is one of the key determinants of tokamak plasma transport. The understanding of stability and transport effects in tokamak plasmas is of crucial importance for the design of fusion devices like ITER. A fully consistent island evolution model should include turbulent (anomalous) transport for the correct calculation of {\it e.g.} radial fluxes and anomalous viscosity (which determines island rotation and hence the stabilizing or destabilizing role of the polarization current). As a first step and a ``proxy'' for turbulent transport, we use a neoclassical model. A neoclassical description allows us to develop a closed model that both consistently includes transport effects on the island growth and provides the appropriate basis for the inclusion of micro-turbulent transport (see [1]). The `true' (anomalous) fluxes can be obtained from a flux-tube turbulence code. The separation of scales (turbulence smaller than the island) and times (turbulent transport faster than the island evolution) allows us to consider the island as a large (relative to the turbulence length scale) and slowly evolving structure for which local flux-tube calculations of transport is appropriate. \newline [1] P. Popovich, S.J. Allfrey and S.C. Cowley, `Transport and the neoclassical tearing mode: Slab geometry' (this conference).   

Tempest simulations of kinetic GAM mode and neoclassical turbulence

TEMPEST is a nonlinear five dimensional (3d2v) gyrokinetic continuum code for studies of H-mode edge plasma neoclassical transport and turbulence in real divertor geometry. The 4D TEMPEST code correctly produces frequency, collisionless damping of GAM and zonal flow with fully nonlinear Boltzmann electrons in homogeneous plasmas. For large q=4 to 9, the Tempest simulations show that a series of resonance at higher harmonics v$_{\vert \vert }=\omega _{G}$qR$_{0}$/n with n=4 become effective. The TEMPEST simulation also shows that GAM exists in edge plasma pedestal for steep density and temperature gradients, and an initial GAM relaxes to the standard neoclassical residual with neoclassical transport, rather than Rosenbluth-Hinton residual due to the presence of ion-ion collisions. The enhanced GAM damping explains experimental BES measurements on the edge q scaling of the GAM amplitude. Our 5D gyrokinetic code is built on 4D Tempest neoclassical code with extension to a fifth dimension in toroidal direction and with 3D domain decompositions. Progress on performing 5D neoclassical turbulence simulations will be reported.   

Toward an implicit Drift-Lorentz mover

In order to efficiently perform particle simulations in systems with widely varying magnetization, we have developed a ``drift-Lorentz mover,'' which interpolates between full particle dynamics and drift kinetics in such a way as to preserve a physically correct gyroradius and particle drifts for both large and small ratios of the timestep to the cyclotron period\footnote{R.H. Cohen, A. Friedman, M. Kireeff Covo, et. al., Phys. Plasmas {\bf 12}, 056708 (2005).}. We are now adding implicitness to the mover and the associated field solver in order to extend the mover's applicability to systems with plasma frequency exceeding the cyclotron frequency. A first step was adding the polarization charge to the field solver and a two-time-level predictor corrector procedure \footnote{R.H. Cohen, A. Friedman, D.P. Grote and J.-L. Vay, Nucl. Inst. Methods A 577, 52 (2007).}. We outline here two approaches to adding further implicitness. In both, we add a direct-implicit algorithm to the Lorentz portion of the mover; the drift portion can then be treated as in Ref. 3, or fully implicitly, with a modified predictor-corrector procedure. We describe the algorithms, stability analyses, and status of implementation.   

Gyrokinetic Models for Edge Plasmas

We summarize a gyrokinetic model for charged-particle species in MFE edge plasmas and address several important issues. 1) The gyrokinetic Vlasov equations should be in conservation form to facilitate a conservative discretization. 2) The differences between the orderings used and results obtained by Qin et. al. [electromagnetic, and targeted to edge plasmas; Phys. Plasmas 14, 056110 (2007)] and Hahm et al. [electrostatic and targeted to core transport barriers; Phys. Plasmas 3, 4658 (1996)] are examined. Both assume that the electric potential is split into a large long-wavelength part and a small-amplitude perturbed part. Qin asserts that his particular form of the second-order potential is needed for energy conservation. 3) We examine practical forms of the gyrokinetic Poisson-Maxwell equations for the case when the perturbations are neither small-amplitude nor long-wavelength. 4) We build on the theoretical formulations of large-amplitude Gyrokinetic Coulomb collision operators (when linearization does not apply; e.g., by Brizard and by Qin et. al.) to develop an operator suitable for numerical implementation.   

Particle-in-cell modelling of plasma deposition in castellated divertor targets

JET and ITER plasma facing components (PFC) are segmented into cells to minimise the mechanical stress that is produced by thermal expansion of the components under plasma/radiative loads. This complex geometry introduces a significant complication in the estimation of the power load of these components, as the gap width can be comparable to the ion Larmor radius. We present results of two-dimensional, self-consistent kinetic simulations of this problem using the SPICE2 code based on a particle-in-cell technique. It has been developed for edge plasma simulations using arbitrary velocity distribution functions. The code is highly optimized and is designed for computationally demanding simulations. The code follows the charged particle trajectories on their way to the PFCs and estimates the plasma deposition in a non-symmetric electric potential. The results of power and particle loads calculations are presented for JET and ITER conditions.   

Simulations of dimensionless parameter experiments using theory-based transport models

Dimensionless plasma parameter analyses are widely recognized as powerful tools for the study of energy and particle confinement, and also provide key quantities for the estimation of performance in future thermonuclear devices. Here we describe transport modelling of dimensionless parameter experiments using the theory-based models GLF23 and MMM95. Firstly, the $\beta$ and $\nu$* dependence of heat transport in the models is determined by running them stand-alone with imposed plasma profiles. In the JET parametric domain used in recent dedicated $\beta$ scan experiments, MMM95 predicts a $\beta$ degradation of confinement caused by the ideal MHD ballooning mode, whereas GLF23, which has a critical $\beta$ value higher than the experimental $\beta $ range, predicts a weak dependence. Secondly, the models are used in ASTRA predictive simulations of Ti and Te in order to test the capability of the models to reproduce experimental results. Despite a reasonable agreement with experimental profiles, the models sensitivity to the dimensionless parameters mismatch throughout the scan may lead to a wrong interpretation of the results. This is checked by running predictive simulations using modified input parameters in order to correct the mismatch.   

Effect of fast-ion loss on momentum transport in tokamak plasmas with toroidal field ripples

One-dimensional transport code, TASK/TX, has been developed to study the plasma rotation and the radial electric field in tokamak plasmas [1]. The code simultaneously solves a set of the two-fluid equations in the quasi-toroidal coordinates coupled with Maxwell's equations and beam-ion slowing down equation. It is observed in JT-60U that the reduction of the toroidal field ripple by installing ferritic steel tiles tends to rotate the plasma in the co direction because the counter rotation caused by the fast-ion loss is suppressed [2]. A model of the ripple loss has been made to study the phenomena and the behavior of the beam ions affected by the ripples can be self-consistently calculated. Numerical solutions reproduce the reduction of the toroidal co-rotation with co and perpendicular NBIs as the ripple amplitude increases. The toroidal rotation varies with the ripple amplitude at constant pressure gradient, as is observed in JT-60U [2], and the radial electric field also changes near the peripheral. This implies the change of the toroidal rotation strongly relates to that of the radial electric field through the radial force balance. \newline [1] M. Honda and A. Fukuyama, submitted to J. Comput. Phys. \newline [2] M. Yoshida, et al., Plasma Phys. Control. Fusion \textbf{48} 1673 (2006).   

Charging and Rotation of Pellet Ablation Cloud

The interior of pellet ablation clouds charge to a negative electric floating potential because the incident plasma ions are stopped in a thin layer at the cloud/plasma interface, and this floating potential varies radially causing $E\times B$ rotation of the cloud with azimuthal velocities of order $v_{\theta}\simeq T_e/B r_c$ [1]. Numerical simulations of this effect with a time-dependent pellet ablation model have been performed using the front tracking based MHD code. The main features of the model include a self-consistent evolving potential distribution in the ablation cloud, inward $J \times B$ forces and outward centrifugal forces, atomic processes, and an improved electrical conductivity model which accounts for direct impact ionization of the cold ablated neutrals by the incident plasma electrons. The major conclusion of the study is that the cloud rotation reaches velocities comparable to ablation sound speeds, and therefore the centrifugal force adds significantly to the pressure gradient forces, thus broadening the width of the field aligned ablation channel. Cloud widening, in turn, reduces the cloud opacity and leads to a 30\% increase in the ablation rate compared to the no rotation case for pellets crossing the pedestal region in ITER. \newline [1] P.B. Parks, Plasma Phys. Control. Fusion 38, (1996) 571.